a. Sine and Cosine are complementary angles of each other. This means that their angles added together measure 90 degrees. In the sense of the Pythagorean Theorem, sin²(A) + cos²(A) = 1. Sin squared plus cosine squared equals 1.
b. Cotangent is the reciprocal of tangent. Cotangent is equal to 1/tangent(theta. Tangent is equal to opposite divided by adjacent. Cotangent is equal to adjacent over opposite.
c. Sine and Cosecant are reciprocals of each other. Cosecant is equal to 1/sin(theta. Sine is equal to opposite over hypotenuse. Cosecant is equal to hypotenuse over opposite.
d. Cosine and Secant are reciprocals of each other. Secant is equal to 1/cos(theta . Cosine is equal to adjacent over hypotenuse. Secant is equal to hypotenuse over adjacent.
e. Sine, Cosine, & Tangent are all ratios based on a right triangle. They help relate the side lengths and angle.
A. Sine and cosine are related to each other. In acute angles, sine theta and cosine theta are the lengths of the legs of a right triangle with a hypotenuse of 1. Applying the Pythagorean Theorem, we see that sin^2 theta + cos^2 theta=1. The sum of the squares of sine and cosine are equal to 1. This relationship applies to all angles, not just acute angles. It is one of the most important equations in trigonometry.
B. Just like sine and cosine, tangent and cotangent are related to each other. Each is the co-function of the other, just like sine and cosine! Like we learned in class, tangent is equaled to y/x and cotangent is the reciprocal x/y.
C. Of course sine and cosecant will be related. Along with tangent and cotangent, they are reciprocals of each other. We know that sine is y/r, so therefore cosecant is r/y.
D. Cosine and secant are just like sine and cosecant. As we know, cosine is x/r. Since they are reciprocals of each other, secant will be r/x.
E. Since, cosine, and tangent are also related to each other. We know that sine tells the length of the y and cosine tells the length of the x. The tangent function takes the y and divides it by x.
It seems like a lot, but every one of the six functions is just one side divided by another. As you can see, it is easy to memorize sine and cosine first. Then, remember the other four functions as combinations of sine and cosine rather than independent functions!
Source: Notebook and Brown, Stan. "The Six Functions (Trig without Tears Part 2)." Oak Road Systems - Software Since 1984. Web. 31 Aug. 2010.
A. Sine and Cosine can both be defined in the coordiante plane. Also, both have to do with to knowing the hypotenuse or "r". When given two points on a graph the x is known relates to Cosine and the the y relates to Sine.
B. Cotangent and Tangent are the reciprocal of each other. Cotangent is x/y and Tangent is y/x. For both they are postive in the 1st and 3rd quadrant and negative in the 2nd and 4th.
C. Sine and Cosecant are also the reciprocal of each other. For both you need your hypotenuse and your y. Sine is y/r and Cosecant is r/y. Both sin and csc are postive in the 1st and 2nd quadrant and negative in the 3rd and 4th.
D. Cosine and Secant are also reciprocal of each other just like Sine and Cosecant. Instead of having a y, you have a x and hypotenuse. Both cos and sec are positive in the 1st and 4th quadrant and negative in the 2nd and 3rd.
E. Sine, Cosine, and Tangent give all points needed. Their ratios relate to the right triangle. They give both the lengths and angles need to find theta.
A.Sine and Cosine are related by the leg lengths on a right triangle. You can plug them into the Pythagorean Theorem and end up with a hypotenuse of 1. (cos^2 theta + sin^2 theta = 1)Cosine related to x, so the formula would be x/hypotenuse. Opposite of cosine is sine, so that formula would be y/hypotenuse.
B.Tangent and cotangent are reciprocals of each other. Tangent is y/x and cotangent is x/y. They both have the same signs in each of the quadrants.
C.Like before, sine and cosecant are also reciprocals of each other. It is the same concept as tangent and cotangent. Sine is y/r and the cosecant is r/y. They also have the same signs in all four of the quadrants.
D.Cosine and secant are related to each other just like the previous two were. They are also reciprocals. The formula you use for these are x/r for cosine and r/x for secant.
E.Sine, cosine, and tangent are all related and give the necessary points you need if you want to find theta. They make up the angles of a right triangle. Sine gives the y, cosine gives the x, and tangent divides the y by x.
*All of these can be found on the trig chart and are very easy to find once you see how they all relate to one another.
A. Sine and Cosine are related in different ways, but the most common way is that you can find both of these on a coordinate plane. Sine takes the length of an angle and tells you the y-component. Cosine takes the length of an angle and tells you the x-component. If you plug this into the Pythagorean Theorem, you will get a hypotenuse of 1. Here is the equation (cos^2theta+ sin^2theta=1). The formula for sine is y/ hypotenuse and the formula for cosine is x/ hypotenuse.
B. Tangent and Cotangent are related because they are simply the reciprocals of each other. When dealing with tangent you use y/x, but when dealing with cotangent you are going to want to use x/y. When in the 1st or the 3rd quadrant they are negative. However, when in the 2nd or 4th quadrant they are positive.
C. Sine and Cosecant are related because they are also reciprocals of each other. It is the exact same thing as tangent and cotangent, just with different letters to represent them. Sine is y/r and cosecant is r/y. When using the coordinate plane they are the opposite of tangent and cotangent; the 1st and 2nd quadrant are positive and the 3rd and 4th quadrant are negative.
D. Cosine and secant ties into all of the others just as the previous ones tied into each other. They are still reciprocals and for both of them you will need to know the hypotenuse and y values. Their signs are both positive in the 1st and 4th and negative in the 2nd and 3rd.
E. As you can see, sine, cosine, and tangent are all related with one another. They can all be found on a coordinate plane and they make up a right triangle. sine=x, cosine=y, and tangent= y/x. This is giving you everything that you need to know in order to find theta.
Make sure you cite your sources. Some of you are mentioning information other than what we have gone over in class. Make sure you cite your source if you find one!!!!
Sine and cosine are related to the x and y axis.They are also inverses .This means that if we know the value of sine for some q, then we can work out the cosine using this formula.
Tangent and cotangent are related because simply inverses.Tangent is equal to y/x, whereas cotangent is x/y. where tangent is positive on the coordinate plane, so is cotangent and vise versa. when cotangent is negative so is tangent.
c.) Sine and Secant
Both sine and secant relate to the y axis. sine= y/r . secant= r/y.Like tangent and cosine, where one is positive , the other will be also and vise versa.
d.)Cosine and Secant The relationship between cosine and secant is like the relationship between tangent and cotangent, and sine and cosine. Both are positive and negative in the same quadrants. Both are also related to the x axis. Cosine=x/r and secant= r/x.
e.) Sine Cosine and Tangent
Sine, cosine, and tangent are used to relate angles to sides of triangles.Sine is related to the y axis (y/r). Cosine is related to the x axis (x/r). Tangent however is related to both the x and y axis (y/x). Together they form triangles which helps you find theta.
A. sine and cosine both share similar values. They come together on the coordinate plane to make up 90 degrees. Their both inverses which means if we know the value for sine then we can easily find cosine.
B. tangent and cotangent are related to each other just like sine and cosine. We learned in class that tangent is y/x and cotangent is x/y.
C. sine and cosecant are found by discovering your hypotenuse. Also you need your y to find sine y/r or y/h and cosecant r/y or h/y.
D. cosine and secant mirror each other even in values. Cosine is expressed as x/r or x/h. Secant is expressed as r/x or h/x.
E. sine, cosine, and tangent all come together to make a triangle. Without these points you won't be able to find theta. Sine has to do with the y axis, cosine has to do with the x axis, and tangent has to do with both in order to make a right triangle.
Once you establish the relationship between all these functions they can be found on the trig chart.
A.Sine and cosine are related to each other. They are both the legs in a right triangle. They are both found in a coordinate plane. Sine tells you the length of the angle. It also follows the y axis. Cosine can also tell you the length of the angle. It follows the x axis.
B.Tangent and Cotangent are the reciprocals of each other. Tangent’s formula is y/x and cotangent is x/y. They have the same signs.
C.Sine and cosecant are also reciprocals of each other. Sine’s formula is y/r, and cosecant’s formula is r/y. they both have the same signs when they are in the same quadrant.
D.Cosine and secant are also the reciprocals of each other. Cosine is x/r, and secant is r/x. they are both negative in the same quadrants, and they are both positive in the same quadrant just like the others.
E.Sine, cosine, and tangent all give the points needed to make a right triangle on a graph. Cosine gives the y, sine gives the y, and tangent gives the y/x.
a. Sine and Cosine are both legs in a triangle. When you add both of them together you get 90 degrees. Sine has to do with the y axis and Cosine has to do with the x axis. They both can tell you the length of the angle.
b. Tangent and Cotangent are related because they are reciprocals to each other. They also both have similar formulas, tangent's formula is y/x and cotangent's formula is x/y.
c. Like tangent and cotangent, sine and co secant are reciprocals to each other. They also have similar formulas, sine's formula is y/r and co secant's formula is r/y.
d. Like the last two points cosine and secant are both reciprocals to each other. They also have similar formulas, cosine's formula is x/r and secant's formula is r/x. Thy also have the same sign if they are in the same quadrant.
e. A triangle is made with sine, cosine, and tangent. All three of these points are used to find theta. Sine is the y axis, cosine is the x axis, and tangent is both.
When graphing sine and cosine, 2 points are given. The x axis is your cosine and the y is your sine. Both Sine and Cosine can be found on the coordinate plane. For both of these you have to know the hypotenuse or “R”.
When graphing for tangent and cotangent, if your point is in the first or third quadrant it will always be positive and when it is in the second or fourth quadrant it will always be negative. Also they are reciprocals of each other. Tangent = y/x and Cotangent = x/y.
For sine and cosecant you need to know the y and the hypotenuse. Just like tangent and cotangent, sine and cosecant are reciprocals. Cosecant = r/y and Sine y/r.
Cosine and secant are very similar to sine and cosecant. You need a hypotenuse and a x just like sine and cosecant have a hypotenuse and a y. Secant = r/x and Cosine = x/r.
You can find sine, cosine, and tangent all on a right triangle. Each point is given as an angle on a right triangle. Sine = y, Cosine = x, and Tangent = y divided by x.
a. Sine (sin) and cosine (cos) are both trigonometric functions. Sin=opposite angle, Cosine=adjacent angle on a right triangle. When dealing with these angle measurements and length y=sinѲ and x=cosѲ. These functions, depending on whether its radians or degrees, will evaluate differently.
b. Tangent (tan) and Cotangent (cot) are reciprocals of one another. When using tangent we use y/x and when using cotangent we use x/y. Both functions follow one another in the quadrants. When in quadrants I and III both tangent and cotangent are positive; however when they are in II and IV they are both negative.
c. Sine and cosecant are reciprocals of one another, just like tan and cot. The formula for (sin) is y/r and the formula for (csc) is r/y. When in the same quadrant, they both are positive, and vice versa.
d. Cosine (cos) and secant (sec) are also reciprocals of one another. The formula for (cos) is x/r and the formula for (sec) is r/x. Just like the others, both are positive in the same quadrant, and vice versa.
e. Sine, Cosine, and Tangent all form the right triangle and make up the points. Cos=x, sin=y, and tan=y/x. All these trig formulas tie together and are related somehow.
a.Sine and cosine are both related to each other. They are known to be both of the leggs in a right triangle. Sine shows you the length of the angle and follows the y axis. Cosine can show you the length of the angle while it follows the x axis
b.Tangent and Cotangent reciprocal each other. Tangent’s formula is y/x and cotangent is x/y. They both have the same signs.
c.Sine and cosecant are also reciprocals of each other. Sin formula is y/r, and cos formula is r/y. They can both have the same signs if in the same quadrant.
d.Cosine and secant are also the reciprocals of each other. Cosine is x/r, and secant is r/x.
e.Sine, cosine, and tangent have the same points needed to make a right triangle. Cosine is the y, sine is the y, and tangent is the y/x.
A. Sine and Cosine can both be found somewhere in the coordinate plane. Also, both can be used to find the hypotenuse. When given two points on a graph the x is used to find to Cosine and the the y is used to find to Sine.
B. Cotangent and Tangent are the opposites of one another. Cotangent is defined as x/y and Tangent is the opposite, y/x. With this nature, both are always positive in Q 1/3 and negative in Q 2/4.
C. Sine and Cosecant similar in relationship to Cot and Tan in the fact that they are reciprocals. For both you need your r and your y. Sine is y/r and Cosecant is r/y.
D. Cosine and Secant are also reciprocals. You have x and your hypotenuse for these. Both cos and sec are positive in the 1st and 4th quadrant and negative in the 2nd and 3rd.
E. Sine, Cosine, and Tangent give all points needed. They form right triangles.
a. Sine and Cosine are related because they are complementary to each other and come together to make a 90 degree angle.(Wikipedia,1) Also on the trig chart the sine values and the cosine values are opposite of each other.
b. Tangent and Cotangent are related because they are the reciprocal of one another. Tangent equals y/x and Cotangent equals x/y. Also on the trig chart Tangents values are opposite of Cotangent values.
c. Sine and Cosecant are related because they are reciprocals of one another. Sine equals y/r and Cosecant equals r/y. Sine and Cosecant also have the same points on the reference angle. Where Sine is 1 so is Cosecant and where Sine is -1 so is Cosecant. The same goes for when Sine is 0.
d. Cosine and Secant are related because they to are the reciprocal of each other. Cosine equals x/r and Secant equals r/x. Just as it went for Sine and Cosecant, Cosine and Secant have the same reference angles on the coordinate plane. Where Cosine equals 1, so does Secant. And so on and so forth.
e. Sine, Cosine, and Tangent are related because tan^-1 and sin^-1 are both b/a. They are also both the reciprocal of cos^-1 which is a/b. Also sin. and cos. can be used to find tangent since sin is y/r , cos is x/, and tangent is y/x.
a. Sine and Cosine are both on the opposite line of the other on the coordinate plane. Sine relates to y and cosine relates to x. Also on the trig chart they are same if you flip the row.
b. Tangent and Cotangent are also the opposite of eachother. Tangent is y/x and cotangent is x/y.
c. Sine and Cosecant are also the receprical of one another. Sine is y/r (r being the hypotenuse) and cosecant is r/y.
d. Cosine and Secant, once more, are the opposites of each other. Cosine being x/r and secant being r/x.
e. Sine, Cosine & Tangent, when the three work together, coherently form the three legs of a triangle.
a. Sine and Cosine are complementary angles of each other. This means that their angles added together measure 90 degrees. In the sense of the Pythagorean Theorem, sin²(A) + cos²(A) = 1. Sin squared plus cosine squared equals 1.
ReplyDeleteb. Cotangent is the reciprocal of tangent. Cotangent is equal to 1/tangent(theta. Tangent is equal to opposite divided by adjacent. Cotangent is equal to adjacent over opposite.
c. Sine and Cosecant are reciprocals of each other. Cosecant is equal to 1/sin(theta. Sine is equal to opposite over hypotenuse. Cosecant is equal to hypotenuse over opposite.
d. Cosine and Secant are reciprocals of each other. Secant is equal to 1/cos(theta . Cosine is equal to adjacent over hypotenuse. Secant is equal to hypotenuse over adjacent.
e. Sine, Cosine, & Tangent are all ratios based on a right triangle. They help relate the side lengths and angle.
This comment has been removed by the author.
ReplyDeleteA. Sine and cosine are related to each other. In acute angles, sine theta and cosine theta are the lengths of the legs of a right triangle with a hypotenuse of 1. Applying the Pythagorean Theorem, we see that sin^2 theta + cos^2 theta=1. The sum of the squares of sine and cosine are equal to 1. This relationship applies to all angles, not just acute angles. It is one of the most important equations in trigonometry.
ReplyDeleteB. Just like sine and cosine, tangent and cotangent are related to each other. Each is the co-function of the other, just like sine and cosine! Like we learned in class, tangent is equaled to y/x and cotangent is the reciprocal x/y.
C. Of course sine and cosecant will be related. Along with tangent and cotangent, they are reciprocals of each other. We know that sine is y/r, so therefore cosecant is r/y.
D. Cosine and secant are just like sine and cosecant. As we know, cosine is x/r. Since they are reciprocals of each other, secant will be r/x.
E. Since, cosine, and tangent are also related to each other. We know that sine tells the length of the y and cosine tells the length of the x. The tangent function takes the y and divides it by x.
It seems like a lot, but every one of the six functions is just one side divided by another. As you can see, it is easy to memorize sine and cosine first. Then, remember the other four functions as combinations of sine and cosine rather than independent functions!
Source: Notebook and Brown, Stan. "The Six Functions (Trig without Tears Part 2)." Oak Road Systems - Software Since 1984. Web. 31 Aug. 2010.
A. Sine and Cosine can both be defined in the coordiante plane. Also, both have to do with to knowing the hypotenuse or "r". When given two points on a graph the x is known relates to Cosine and the the y relates to Sine.
ReplyDeleteB. Cotangent and Tangent are the reciprocal of each other. Cotangent is x/y and Tangent is y/x. For both they are postive in the 1st and 3rd quadrant and negative in the 2nd and 4th.
C. Sine and Cosecant are also the reciprocal of each other. For both you need your hypotenuse and your y. Sine is y/r and Cosecant is r/y. Both sin and csc are postive in the 1st and 2nd quadrant and negative in the 3rd and 4th.
D. Cosine and Secant are also reciprocal of each other just like Sine and Cosecant. Instead of having a y, you have a x and hypotenuse. Both cos and sec are positive in the 1st and 4th quadrant and negative in the 2nd and 3rd.
E. Sine, Cosine, and Tangent give all points needed. Their ratios relate to the right triangle. They give both the lengths and angles need to find theta.
A.Sine and Cosine are related by the leg lengths on a right triangle. You can plug them into the Pythagorean Theorem and end up with a hypotenuse of 1. (cos^2 theta + sin^2 theta = 1)Cosine related to x, so the formula would be x/hypotenuse. Opposite of cosine is sine, so that formula would be y/hypotenuse.
ReplyDeleteB.Tangent and cotangent are reciprocals of each other. Tangent is y/x and cotangent is x/y. They both have the same signs in each of the quadrants.
C.Like before, sine and cosecant are also reciprocals of each other. It is the same concept as tangent and cotangent. Sine is y/r and the cosecant is r/y. They also have the same signs in all four of the quadrants.
D.Cosine and secant are related to each other just like the previous two were. They are also reciprocals. The formula you use for these are x/r for cosine and r/x for secant.
E.Sine, cosine, and tangent are all related and give the necessary points you need if you want to find theta. They make up the angles of a right triangle. Sine gives the y, cosine gives the x, and tangent divides the y by x.
*All of these can be found on the trig chart and are very easy to find once you see how they all relate to one another.
A. Sine and Cosine are related in different ways, but the most common way is that you can find both of these on a coordinate plane. Sine takes the length of an angle and tells you the y-component. Cosine takes the length of an angle and tells you the x-component. If you plug this into the Pythagorean Theorem, you will get a hypotenuse of 1. Here is the equation (cos^2theta+ sin^2theta=1). The formula for sine is y/ hypotenuse and the formula for cosine is x/ hypotenuse.
ReplyDeleteB. Tangent and Cotangent are related because they are simply the reciprocals of each other. When dealing with tangent you use y/x, but when dealing with cotangent you are going to want to use x/y. When in the 1st or the 3rd quadrant they are negative. However, when in the 2nd or 4th quadrant they are positive.
C. Sine and Cosecant are related because they are also reciprocals of each other. It is the exact same thing as tangent and cotangent, just with different letters to represent them. Sine is y/r and cosecant is r/y. When using the coordinate plane they are the opposite of tangent and cotangent; the 1st and 2nd quadrant are positive and the 3rd and 4th quadrant are negative.
D. Cosine and secant ties into all of the others just as the previous ones tied into each other. They are still reciprocals and for both of them you will need to know the hypotenuse and y values. Their signs are both positive in the 1st and 4th and negative in the 2nd and 3rd.
E. As you can see, sine, cosine, and tangent are all related with one another. They can all be found on a coordinate plane and they make up a right triangle. sine=x, cosine=y, and tangent= y/x. This is giving you everything that you need to know in order to find theta.
Make sure you cite your sources. Some of you are mentioning information other than what we have gone over in class. Make sure you cite your source if you find one!!!!
ReplyDeletea.) sine and cosine
ReplyDeleteSine and cosine are related to the x and y axis.They are also inverses .This means that if we know the value of sine for some q, then we can work out the cosine using this formula.
(Trigonmetric Relationships)
b.) Tangent and Cotangent
Tangent and cotangent are related because simply inverses.Tangent is equal to y/x, whereas cotangent is x/y. where tangent is positive on the coordinate plane, so is cotangent and vise versa. when cotangent is negative so is tangent.
c.) Sine and Secant
Both sine and secant relate to the y axis. sine= y/r . secant= r/y.Like tangent and cosine, where one is positive , the other will be also and vise versa.
d.)Cosine and Secant
The relationship between cosine and secant is like the relationship between tangent and cotangent, and sine and cosine. Both are positive and negative in the same quadrants. Both are also related to the x axis. Cosine=x/r and secant= r/x.
e.) Sine Cosine and Tangent
Sine, cosine, and tangent are used to relate angles to sides of triangles.Sine is related to the y axis (y/r). Cosine is related to the x axis (x/r). Tangent however is related to both the x and y axis (y/x). Together they form triangles which helps you find theta.
(Wikipedia)
A. sine and cosine both share similar values. They come together on the coordinate plane to make up 90 degrees. Their both inverses which means if we know the value for sine then we can easily find cosine.
ReplyDeleteB. tangent and cotangent are related to each other just like sine and cosine. We learned in class that tangent is y/x and cotangent is x/y.
C. sine and cosecant are found by discovering your hypotenuse. Also you need your y to find sine y/r or y/h and cosecant r/y or h/y.
D. cosine and secant mirror each other even in values. Cosine is expressed as x/r or x/h. Secant is expressed as r/x or h/x.
E. sine, cosine, and tangent all come together to make a triangle. Without these points you won't be able to find theta. Sine has to do with the y axis, cosine has to do with the x axis, and tangent has to do with both in order to make a right triangle.
Once you establish the relationship between all these functions they can be found on the trig chart.
A.Sine and cosine are related to each other. They are both the legs in a right triangle. They are both found in a coordinate plane. Sine tells you the length of the angle. It also follows the y axis. Cosine can also tell you the length of the angle. It follows the x axis.
ReplyDeleteB.Tangent and Cotangent are the reciprocals of each other. Tangent’s formula is y/x and cotangent is x/y. They have the same signs.
C.Sine and cosecant are also reciprocals of each other. Sine’s formula is y/r, and cosecant’s formula is r/y. they both have the same signs when they are in the same quadrant.
D.Cosine and secant are also the reciprocals of each other. Cosine is x/r, and secant is r/x. they are both negative in the same quadrants, and they are both positive in the same quadrant just like the others.
E.Sine, cosine, and tangent all give the points needed to make a right triangle on a graph. Cosine gives the y, sine gives the y, and tangent gives the y/x.
a. Sine and Cosine are both legs in a triangle. When you add both of them together you get 90 degrees. Sine has to do with the y axis and Cosine has to do with the x axis. They both can tell you the length of the angle.
ReplyDeleteb. Tangent and Cotangent are related because they are reciprocals to each other. They also both have similar formulas, tangent's formula is y/x and cotangent's formula is x/y.
c. Like tangent and cotangent, sine and co secant are reciprocals to each other. They also have similar formulas, sine's formula is y/r and co secant's formula is r/y.
d. Like the last two points cosine and secant are both reciprocals to each other. They also have similar formulas, cosine's formula is x/r and secant's formula is r/x. Thy also have the same sign if they are in the same quadrant.
e. A triangle is made with sine, cosine, and tangent. All three of these points are used to find theta. Sine is the y axis, cosine is the x axis, and tangent is both.
When graphing sine and cosine, 2 points are given. The x axis is your cosine and the y is your sine. Both Sine and Cosine can be found on the coordinate plane. For both of these you have to know the hypotenuse or “R”.
ReplyDeleteWhen graphing for tangent and cotangent, if your point is in the first or third quadrant it will always be positive and when it is in the second or fourth quadrant it will always be negative. Also they are reciprocals of each other. Tangent = y/x and Cotangent = x/y.
For sine and cosecant you need to know the y and the hypotenuse. Just like tangent and cotangent, sine and cosecant are reciprocals. Cosecant = r/y and Sine y/r.
Cosine and secant are very similar to sine and cosecant. You need a hypotenuse and a x just like sine and cosecant have a hypotenuse and a y. Secant = r/x and Cosine = x/r.
You can find sine, cosine, and tangent all on a right triangle. Each point is given as an angle on a right triangle. Sine = y, Cosine = x, and Tangent = y divided by x.
This comment has been removed by the author.
ReplyDeletea. Sine (sin) and cosine (cos) are both trigonometric functions. Sin=opposite angle, Cosine=adjacent angle on a right triangle. When dealing with these angle measurements and length y=sinѲ and x=cosѲ. These functions, depending on whether its radians or degrees, will evaluate differently.
ReplyDeleteb. Tangent (tan) and Cotangent (cot) are reciprocals of one another. When using tangent we use y/x and when using cotangent we use x/y. Both functions follow one another in the quadrants. When in quadrants I and III both tangent and cotangent are positive; however when they are in II and IV they are both negative.
c. Sine and cosecant are reciprocals of one another, just like tan and cot. The formula for (sin) is y/r and the formula for (csc) is r/y. When in the same quadrant, they both are positive, and vice versa.
d. Cosine (cos) and secant (sec) are also reciprocals of one another. The formula for (cos) is x/r and the formula for (sec) is r/x. Just like the others, both are positive in the same quadrant, and vice versa.
e. Sine, Cosine, and Tangent all form the right triangle and make up the points. Cos=x, sin=y, and tan=y/x. All these trig formulas tie together and are related somehow.
a.Sine and cosine are both related to each other. They are known to be both of the leggs in a right triangle. Sine shows you the length of the angle and follows the y axis. Cosine can show you the length of the angle while it follows the x axis
ReplyDeleteb.Tangent and Cotangent reciprocal each other. Tangent’s formula is y/x and cotangent is x/y. They both have the same signs.
c.Sine and cosecant are also reciprocals of each other. Sin formula is y/r, and cos formula is r/y. They can both have the same signs if in the same quadrant.
d.Cosine and secant are also the reciprocals of each other. Cosine is x/r, and secant is r/x.
e.Sine, cosine, and tangent have the same points needed to make a right triangle. Cosine is the y, sine is the y, and tangent is the y/x.
A. Sine and Cosine can both be found somewhere in the coordinate plane. Also, both can be used to find the hypotenuse. When given two points on a graph the x is used to find to Cosine and the the y is used to find to Sine.
ReplyDeleteB. Cotangent and Tangent are the opposites of one another. Cotangent is defined as x/y and Tangent is the opposite, y/x. With this nature, both are always positive in Q 1/3 and negative in Q 2/4.
C. Sine and Cosecant similar in relationship to Cot and Tan in the fact that they are reciprocals. For both you need your r and your y. Sine is y/r and Cosecant is r/y.
D. Cosine and Secant are also reciprocals. You have x and your hypotenuse for these. Both cos and sec are positive in the 1st and 4th quadrant and negative in the 2nd and 3rd.
E. Sine, Cosine, and Tangent give all points needed. They form right triangles.
a. Sine and Cosine are related because they are complementary to each other and come together to make a 90 degree angle.(Wikipedia,1) Also on the trig chart the sine values and the cosine values are opposite of each other.
ReplyDeleteb. Tangent and Cotangent are related because they are the reciprocal of one another. Tangent equals y/x and Cotangent equals x/y. Also on the trig chart Tangents values are opposite of Cotangent values.
c. Sine and Cosecant are related because they are reciprocals of one another. Sine equals y/r and Cosecant equals r/y. Sine and Cosecant also have the same points on the reference angle. Where Sine is 1 so is Cosecant and where Sine is -1 so is Cosecant. The same goes for when Sine is 0.
d. Cosine and Secant are related because they to are the reciprocal of each other. Cosine equals x/r and Secant equals r/x. Just as it went for Sine and Cosecant, Cosine and Secant have the same reference angles on the coordinate plane. Where Cosine equals 1, so does Secant. And so on and so forth.
e. Sine, Cosine, and Tangent are related because tan^-1 and sin^-1 are both b/a. They are also both the reciprocal of cos^-1 which is a/b. Also sin. and cos. can be used to find tangent since sin is y/r , cos is x/, and tangent is y/x.
a. Sine and Cosine are both on the opposite line of the other on the coordinate plane. Sine relates to y and cosine relates to x. Also on the trig chart they are same if you flip the row.
ReplyDeleteb. Tangent and Cotangent are also the opposite of eachother. Tangent is y/x and cotangent is x/y.
c. Sine and Cosecant are also the receprical of one another. Sine is y/r (r being the hypotenuse) and cosecant is r/y.
d. Cosine and Secant, once more, are the opposites of each other. Cosine being x/r and secant being r/x.
e. Sine, Cosine & Tangent, when the three work together, coherently form the three legs of a triangle.