In chapter 7 we learned about the unit circle. The unit circle relates to trigonometric functions. Now, in chapter 9 we’re learning about triangles and SOHCAHTOA which is related to the unit circle. SOHCAHTOA is used to solve right triangles.
In mathematics, the unit circle is a circle with the radius of one. The unit circle is the circle of radius one centered at the origin which is (0,0). If (x, y) is a point on the unit circle in the first quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. Therefore, by the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA.
Triangles constructed on the unit circle can also be used to illustrate the periodicity of the trigonometric functions.
We learned about SOHCAHTOA and the unit circle this nine weeks, and they actually both relate to each other besides being a part of trigonometry. In chapter 7 we went over the unit circle. It is degrees in radians that make a complete circle. SOHCAHTOA is in chapter 9, and it is used to find measurements of angles in a right triangle.
Since you can only use SOHCAHTOA on a right triangle, that means at least one of the degrees of an angle has to be 90. You can graph sin, cos, and tan on a graph using a unit circle because they share its degrees in common. All triangle’s degrees add up to equal 180. When it is graphed, it will be done on the second quadrant of the circle because that is where the 90-180 degrees is represented.
It is pretty complicated and I had to re-read my resource a few times. Hopefully it’s the right information.
In the first nine weeks of advanced math we learned about some trigonometry. In chapter seven we learned about the unit circle. The unit circle is a circle with a radius of one. In chapter nine we learned about SOHCAHTOA. SOHCAHTOA is used to solve right triangles. We are now going to look at how the two are related to one another.
The unit circle and SOHCAHTOA all have to do with graphing with sine, cosine, and tangent. Since SOHCAHTOA is only used to solve right triangles one of the angles must be a 90 degree angle. Graphing sine, cosine, and tangent on a unit circle is possible because they both involve a common degree. Triangles add up to 180 and half of the unit circle is 180. When graphing on the unit circle you must decide what quadrant it is in. If you are graphing a number between 90 and 180 you will graph in the 2nd quadrant.
You use SOHCAHTOA is solve right triangles and the unit circle is close to trigonometry functions. Both are related in some ways. Theres more to it than just being parts of trigonometry.
With SOHCAHTOA you solve right triangles which means one angle must be 90 degrees. You can graph sine, cosine, and tangent using a unit circle. One thing they have in common is there degrees. Both are able to use degrees as long as they add to 180 degrees. You can use the unit circle to decide where to graph your right triangle. It helps you decide what quandrant its in and whether its positive or negative.
To solve right triangles with one angle that must be 90 degrees, you must SOHCAHTOA. You can graph sine, cosine, and tangent using a unit circle. One thing they have in common is there degrees. Both are able to use degrees as long as they add to 180 degrees. You can use the unit circle to decide where to graph your right triangle. It helps you decide what quandrant its in and whether its positive or negative. You can graph sin, cos, and tan on a graph using a unit circle because they share its degrees in common.
All triangle degrees add up to equal 180. When it is graphed, it will be done on the second quadrant of the circle because that is where the 90-180 degrees is represented. Triangles add up to 180 and half of the unit circle is 180. When graphing on the unit circle you must decide what quadrant it is in. If you are graphing a number between 90 and 180 you will graph in the 2nd quadrant.
The unit cirle and SOHCAHTOA are alike in many diffent ways. It was hard to find info on this but this is what i got.
In mathematics, the unit circle is a circle with the radius of one. The unit circle is the circle of radius one centered at the origin which is (0,0). If (x, y) is a point on the unit circle in the first quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. Therefore, by the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA.
In Trigonometry and geometry the unit circle and SOHCAHTOA are used. SOHCAHTOA stand for sin = opposite leg / hypotenuse , Cos = adjacent leg / hypotenuse , And tan = opposite leg / adjacent leg. It can only be used if there is a right angle in the triangle. They can both be used to find angles on a triangle or graph. You can use sine, cosine, and tangent to graph using the unit circle. The thing that they have in common is that they are both in degrees. They both can use degrees as long as they add to 180 degrees. The unit circle can be used to decide where to graph your right triangle. It helps you decide whether it’s positive or negative and it helps you decide what quadrant it’s in. A triangle adds up to one hundred and eighty degrees and so does half of the unit circle. http:// en.wikipedia.org/ wiki /Sohcahtoa#Mnemonics http:// en.wikipedia.org/ wiki/ Trigonometry
In the beginning of the year we learned chapter seven which discussed various things such as degree conversions, radians, and even the unit circle. The unit circle is a circle with a radius of one. It is centered on the coordinate plane with the origin directly in the middle. The unit circle is helpful with the graphing of trigonometry, and the solving of trigonometric functions. This is one factor that the unit circle and sohcahtoa share. Sohcahtoa is an acronym for the trig functions: S: opp/hyp C: adj/hyp T: opp/adj . This is helpful with trigonometry, but may only be used with right triangles. Sohcahtoa is used to help solve right triangles. The unit circle is also. Therefore the unit circle and sohcahtoa are both helpful when solving triangles.when solving a triangle using the Imyy circle you graph it on the coordinate plane. Because you are using the unit circle the legs must be one which heeds the hypotenuse to be the sqr.rt of two. Then you use sohcahtoa to solve for the left over unknowns.
Towards the beginning of the year we learned Chapter 7. This chapter included the unit circle. The Unit Circle has a radius of 1. At 90 degrees the unit circle is (0,1). At 180 degrees the unit circle is (-1,0). At 270 degrees the unit circle is (0,-1). At 360 degrees the unit circle is (1,0). The Unit Circle is helpful when trying to find trigonometric functions. This week and last week we learned Chapter 9. In Chapter 9 we learned SOHCAHTOA. SOHCAHTOA helps to remember what trig functions are equal to in right triangles. SOHCAHTOA means: SIN=opposite/hypotenuse, COS= adjacent/hypotenuse, TAN=opposite/adjacent. CSC is opposite of SIN, SEC is opposite of Cosine, COT is opposite of tangent.
SOHCAHTOA and The Unit Circle are alike because they are both devices to make trigonometry easier. These are shortcuts, that we will need in the future. The ACT is timed and we can use these as tools and get the problems done way quicker and easier.
In chapter 7 we learned about unit circles. The unit circle is related to the trigonometric functions. In chapter 9 we learned about SOHCOHTOA. SOHCOHTOA is used when dealing with a right triangle and having to solve a right triangle. It is used to find the measurement of angles in a triangle while using SOHCOHTOA. SOHCOHTOA stands for S: opp/hyp C: adj/hyp T: opp/adj.
In mathematics, the unit circle is a circle with one radius. The unit circle is a circle of radius one centered at the origin (0, 0). If (x,y) is a point on the unit circle in the 1st quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. When using the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA. When dealing with unit circles you can graph sine, cosine, and tangent using a unit circle, common is there degrees. Both are able to use degrees as long as they add to 180 degrees. Unit circle is decided where to graph it because it can be negative or positive
In chapter 7 we learned about the unit circle. The unit circle relates to trigonometric functions. Now, in chapter 9 we’re learning about triangles and SOHCAHTOA which is related to the unit circle. SOHCAHTOA is used to solve right triangles.
ReplyDeleteIn mathematics, the unit circle is a circle with the radius of one. The unit circle is the circle of radius one centered at the origin which is (0,0). If (x, y) is a point on the unit circle in the first quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. Therefore, by the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA.
Triangles constructed on the unit circle can also be used to illustrate the periodicity of the trigonometric functions.
http://en.wikipedia.org/wiki/Unit_circle
We learned about SOHCAHTOA and the unit circle this nine weeks, and they actually both relate to each other besides being a part of trigonometry. In chapter 7 we went over the unit circle. It is degrees in radians that make a complete circle. SOHCAHTOA is in chapter 9, and it is used to find measurements of angles in a right triangle.
ReplyDeleteSince you can only use SOHCAHTOA on a right triangle, that means at least one of the degrees of an angle has to be 90. You can graph sin, cos, and tan on a graph using a unit circle because they share its degrees in common. All triangle’s degrees add up to equal 180. When it is graphed, it will be done on the second quadrant of the circle because that is where the 90-180 degrees is represented.
It is pretty complicated and I had to re-read my resource a few times. Hopefully it’s the right information.
http://en.wikipedia.org/wiki/Trigonometry
In the first nine weeks of advanced math we learned about some trigonometry. In chapter seven we learned about the unit circle. The unit circle is a circle with a radius of one. In chapter nine we learned about SOHCAHTOA. SOHCAHTOA is used to solve right triangles. We are now going to look at how the two are related to one another.
ReplyDeleteThe unit circle and SOHCAHTOA all have to do with graphing with sine, cosine, and tangent. Since SOHCAHTOA is only used to solve right triangles one of the angles must be a 90 degree angle. Graphing sine, cosine, and tangent on a unit circle is possible because they both involve a common degree. Triangles add up to 180 and half of the unit circle is 180. When graphing on the unit circle you must decide what quadrant it is in. If you are graphing a number between 90 and 180 you will graph in the 2nd quadrant.
http://en.wikipedia.org/wiki/Trigonometry
http://en.wikipedia.org/wiki/Unit_circle
You use SOHCAHTOA is solve right triangles and the unit circle is close to trigonometry functions. Both are related in some ways. Theres more to it than just being parts of trigonometry.
ReplyDeleteWith SOHCAHTOA you solve right triangles which means one angle must be 90 degrees. You can graph sine, cosine, and tangent using a unit circle. One thing they have in common is there degrees. Both are able to use degrees as long as they add to 180 degrees. You can use the unit circle to decide where to graph your right triangle. It helps you decide what quandrant its in and whether its positive or negative.
http://en.wikipedia.org/wiki/Trigonometry
To solve right triangles with one angle that must be 90 degrees, you must SOHCAHTOA. You can graph sine, cosine, and tangent using a unit circle. One thing they have in common is there degrees. Both are able to use degrees as long as they add to 180 degrees. You can use the unit circle to decide where to graph your right triangle. It helps you decide what quandrant its in and whether its positive or negative. You can graph sin, cos, and tan on a graph using a unit circle because they share its degrees in common.
ReplyDeleteAll triangle degrees add up to equal 180. When it is graphed, it will be done on the second quadrant of the circle because that is where the 90-180 degrees is represented. Triangles add up to 180 and half of the unit circle is 180. When graphing on the unit circle you must decide what quadrant it is in. If you are graphing a number between 90 and 180 you will graph in the 2nd quadrant.
http://en.wikipedia.org/wiki/Trigonometry
The unit cirle and SOHCAHTOA are alike in many diffent ways. It was hard to find info on this but this is what i got.
ReplyDeleteIn mathematics, the unit circle is a circle with the radius of one. The unit circle is the circle of radius one centered at the origin which is (0,0). If (x, y) is a point on the unit circle in the first quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. Therefore, by the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA.
http://en.wikipedia.org/wiki/Unit_circle
In Trigonometry and geometry the unit circle and SOHCAHTOA are used. SOHCAHTOA stand for sin = opposite leg / hypotenuse , Cos = adjacent leg / hypotenuse , And tan = opposite leg / adjacent leg. It can only be used if there is a right angle in the triangle. They can both be used to find angles on a triangle or graph. You can use sine, cosine, and tangent to graph using the unit circle. The thing that they have in common is that they are both in degrees. They both can use degrees as long as they add to 180 degrees. The unit circle can be used to decide where to graph your right triangle. It helps you decide whether it’s positive or negative and it helps you decide what quadrant it’s in. A triangle adds up to one hundred and eighty degrees and so does half of the unit circle.
ReplyDeletehttp:// en.wikipedia.org/ wiki /Sohcahtoa#Mnemonics
http:// en.wikipedia.org/ wiki/ Trigonometry
In the beginning of the year we learned chapter seven which discussed various things such as degree conversions, radians, and even the unit circle. The unit circle is a circle with a radius of one. It is centered on the coordinate plane with the origin directly in the middle. The unit circle is helpful with the graphing of trigonometry, and the solving of trigonometric functions. This is one factor that the unit circle and sohcahtoa share. Sohcahtoa is an acronym for the trig functions: S: opp/hyp C: adj/hyp T: opp/adj . This is helpful with trigonometry, but may only be used with right triangles.
ReplyDeleteSohcahtoa is used to help solve right triangles. The unit circle is also. Therefore the unit circle and sohcahtoa are both helpful when solving triangles.when solving a triangle using the Imyy circle you graph it on the coordinate plane. Because you are using the unit circle the legs must be one which heeds the hypotenuse to be the sqr.rt of two. Then you use sohcahtoa to solve for the left over unknowns.
Towards the beginning of the year we learned Chapter 7. This chapter included the unit circle. The Unit Circle has a radius of 1. At 90 degrees the unit circle is (0,1). At 180 degrees the unit circle is (-1,0). At 270 degrees the unit circle is (0,-1). At 360 degrees the unit circle is (1,0). The Unit Circle is helpful when trying to find trigonometric functions. This week and last week we learned Chapter 9. In Chapter 9 we learned SOHCAHTOA. SOHCAHTOA helps to remember what trig functions are equal to in right triangles. SOHCAHTOA means: SIN=opposite/hypotenuse, COS= adjacent/hypotenuse, TAN=opposite/adjacent. CSC is opposite of SIN, SEC is opposite of Cosine, COT is opposite of tangent.
ReplyDeleteSOHCAHTOA and The Unit Circle are alike because they are both devices to make trigonometry easier. These are shortcuts, that we will need in the future. The ACT is timed and we can use these as tools and get the problems done way quicker and easier.
In chapter 7 we learned about unit circles. The unit circle is related to the trigonometric functions. In chapter 9 we learned about SOHCOHTOA. SOHCOHTOA is used when dealing with a right triangle and having to solve a right triangle. It is used to find the measurement of angles in a triangle while using SOHCOHTOA. SOHCOHTOA stands for S: opp/hyp C: adj/hyp T: opp/adj.
ReplyDeleteIn mathematics, the unit circle is a circle with one radius. The unit circle is a circle of radius one centered at the origin (0, 0). If (x,y) is a point on the unit circle in the 1st quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has a length of 1. When using the Pythagorean Theorem x and y satisfy the equation x^2 + y^2=1. Since x^2 = -(x^2) for all x, and since the reflection of any point on the unit circle about the x or y axis is also on the unit circle, the above equation holds for all points (x, y) on the unit circle, not just those in the first quadrant. That is one connection between the unit circle and SOHCAHTOA.
When dealing with unit circles you can graph sine, cosine, and tangent using a unit circle, common is there degrees. Both are able to use degrees as long as they add to 180 degrees. Unit circle is decided where to graph it because it can be negative or positive
http://en.wikipedia.org/wiki/Unit_circle