Come up with your own trig graphing problem and walk someone through it step by step explaining each step and formula as though they have never taken Advanced Math.
There are many different types of trig graphing problems, but the one I am going to do is how to find a reference angle. Finding a reference angle is very simple if you follow the steps that are given.
Example: Find the reference angle of sin565 1. The first step is to find out what quadrant on the coordinate plane it is on.
2. You will take the number 565 and subtract it by 360, so you will come up with an answer that is between 0 and 360 degrees.
3. The answer you will come up with is 205, which is in the third quadrant.
4. Since sin represents the y axis ( vertical line ), you check to see if sin is positive or negative in the third quadrant.
5. Sin turns out to be negative in the third quadrant so the first part of your answer will look like this: - sin ( here is where you will place the number you get )
6. To get the last part of your answer, you will take 205 and subtract it by 90 until you get a number between 0 and 90 degrees.
So far in Advanced Math, we’ve learned various types of trigonometry graphing problems. The one I’m going to explain is how to find a coterminal angle.
Keep in mind that you’re plotting these angles on a coordinate plane. A coordinate plane is 360 degrees. Coterminal angles are found by adding or subtracting 360 degrees or 2pi.
EXAMPLE 1: Find a positive and a negative coterminal angle to -200 degrees. A). *REMEMBER: There can be an infinite number of answers to this question. B). First, let’s find a positive coterminal angle. Do this by adding 360 degrees: -200 + 360 = 160 degrees. C). Now, let’s find a negative coterminal angle. Do this by subtracting 360 degrees; -200 – 360 = -560 degrees.
EXAMPLE 2: Find a positive and negative coterminal angle to 2pi/3. A). By using our radians to degrees formula, we know that 2pi/3 = 120 degrees. (2pi/3 x 180/pi, pis cancel). B). Now, add 360 to 120 to get a positive cotermial angle: 480 degrees. C). To find a negative coterminal angle, subtract 360 from 120: -240 degrees. D). We’ve found our positive and negative coterminal angles, now let’s convert them to radians.(degrees x pi/180) E). Positive: 8pi/3 and Negative: -4pi/3
In trig they have many different types of graphing problems. I am going to teach you how to find all six trig functions. You are going to need to know that sin=y/r cos=x/r tan=y/x csc=r/y sec=r/x and cot=x/y. Now we can begin now that you know the formulas you will need to use.
EXAMPLE: Find all six trig functions when given y=24 x=25 Well this is a triple so i know the other number is 7 but if you do not know then you will have to find the other number with Pythagorean and theorem. sin=24/7 cos=25/7 tan=24/25 csc=7/24 sec=7/25 and cot=25/24.
This is the easiest way I can explain it if you dont get mrs. robinson can teach you.. she is a GREAT teacher :)
Graphing is essential in Advanced Math and is used for many different things. This past year we have learned many different ways to solve different problems which often included graphing. One of the first ways we learned to use graphing was when we learned trigonometry and using the inverse function. Here is an example of how to solve such a problem..
Find sin A in the triangle A where r=41 x=40 1. draw your coordinate plane and graph your triangle. We know that that the sides of this triangle form a pythagorean triple; 9,40,41 therefore sine A is 9/41.
Graphing inverses are simple. here is an example.. triangle; a=2 b=2 c=sqrt16 tan=y/x= 2/2 = 1 1, because tan 1 is on our trig chart, we know that its inverse is 45. 2. 45 is in the first quadrant because it is less than 90 degrees. 3. if you wanted to move this angle you would make it neg. and add 180 for the 2nd quad. add 180 for the 3rd quad. and make it neg. and add 360 for 4th quad.
In trig they have many different types of graphing problems, but I’m going teach you how to find all six trig functions. The six trig functions are: sin=y/r, cos=x/r, tan=y/x, csc=r/y, sec=r/x and cot=x/y
Example: Find all six trig functions: given y=4 x= 3 This is a triple the answer is 5, but if you do not know then you will have to find the other number with Pythagorean and theorem. Now to find all the six functions
Sin=4/5 Cos=3/5 Tan= 4/3 Cot= ¾ Csc=5/4 Sec= 5/3
This is the simpliest thing ever if you know what your are doing and I got taught by the master of all math to learn how to do this and her name is Mrs. Robinson. Enjoy =)
In trig there are many graphs which all differ from one another, but in this particular graph I will show you have to find a reference point on the unit circle.
The unit cirle is found on a coordinate plane and has specific points on the angles 90 degrees (0,1), 180 degrees (-1,0), 270 degrees (0,-1), and 360 degrees(1,0).
For Example:
Given Tan270 degrees 1.Go to 270 degrees on the unit circle and the points are (0,-1).
2. For tanget we know it is y/x, so you plug -1/0.
3. Divide -1/0 and you get 0.
4. So the answer is 0, which is a reference angle of tan 270 degrees.
** You could have also looked on your trig chart and just subtracted 180 from 270 until you got something with an absolute value 0 to 90 and looked on the trig chart.
I may have done this blog wrong but I tried to do soemthing different from everyone else.
Our Equation We want to graph the equation 8 cos(3x+π/2)-3. To do this, we’re first going to break it down into a formula with just variables in it. This equation will be Acos(Bx+C)-D.
Explanation of Variables -Amplitude is half of the distance between the maximum and minimum values of the trigonometric curve. -The vertical shift is the amount that the graph will move up or down from the original position of the graph. -The period is the interval between each repetition of the function. -The phase shift is the amount that a trigonometric graph shifts on its horizontal axis.
Calculate Variables -Amplitude is the variable A in our equation, so our amplitude in this case will be 8. -The vertical shift for our equation will be D in our variable equation, which equates to -3. -The period will be 2π/B, or 2π/3. -The phase shift is C/B, or π/6.
Graphing the Function -When graphing the function, we know that it is a cosine trigonometric function. -We also know that the height of the entire curve from the maximum to the minimum is 16, because our amplitude is 8, which is half of the entire height. -Also, the graph will be shifted down 3 due to our vertical shift, telling us that our max is 5 and our min is -11. -We know that our period is 2π/3, so if we divide this by 2, we get the halfway point being 2π/6, if we do the same thing again, we get our 25% point being π/6. Now, since we have the 25% point, we can add it to the halfway point, giving us 3π/6. We now have our five points as being 0, π/6, 2π/6, 3π/6, and 2π/3. -We know that we need to shift our graph horizontally the right by π/6 radians. -Now that we have the horizontal shift, we can add it to all of our 5 points and get our final X coordinates of the points. These are: π/6, 2π/6, 3π/6, 4π/6, and finally 5π/6. -With our X coordinates of our critical points known, we can add the Y coordinates, giving us the final critical points of our cosine graph: (π/6, 5) (2π/6, 0) (3π/6, -11) (4π/6, -0) (5π/6, 5) -Our last step is to add the graph of cosine, crossing the X-axis at the specified critical points above, starting at (π/6, 5).
Okay so this will be my best holiday blog prompt because my wonderful big brother helped me!
There are many different types of trig graphing problems, but the one I am going to do is how to find a reference angle. Finding a reference angle is very simple if you follow the steps that are given.
ReplyDeleteExample: Find the reference angle of sin565
1. The first step is to find out what quadrant on the coordinate plane it is on.
2. You will take the number 565 and subtract it by 360, so you will come up with an answer that is between 0 and 360 degrees.
3. The answer you will come up with is 205, which is in the third quadrant.
4. Since sin represents the y axis ( vertical line ), you check to see if sin is positive or negative in the third quadrant.
5. Sin turns out to be negative in the third quadrant so the first part of your answer will look like this: - sin ( here is where you will place the number you get )
6. To get the last part of your answer, you will take 205 and subtract it by 90 until you get a number between 0 and 90 degrees.
7. Once you subtract 90, you end up with 25.
8. Final answer is: -sin25
This comment has been removed by the author.
ReplyDeleteSo far in Advanced Math, we’ve learned various types of trigonometry graphing problems. The one I’m going to explain is how to find a coterminal angle.
ReplyDeleteKeep in mind that you’re plotting these angles on a coordinate plane. A coordinate plane is 360 degrees.
Coterminal angles are found by adding or subtracting 360 degrees or 2pi.
EXAMPLE 1: Find a positive and a negative coterminal angle to -200 degrees.
A). *REMEMBER: There can be an infinite number of answers to this question.
B). First, let’s find a positive coterminal angle. Do this by adding 360 degrees: -200 + 360 = 160 degrees.
C). Now, let’s find a negative coterminal angle. Do this by subtracting 360 degrees; -200 – 360 = -560 degrees.
EXAMPLE 2: Find a positive and negative coterminal angle to 2pi/3.
A). By using our radians to degrees formula, we know that 2pi/3 = 120 degrees. (2pi/3 x 180/pi, pis cancel).
B). Now, add 360 to 120 to get a positive cotermial angle: 480 degrees.
C). To find a negative coterminal angle, subtract 360 from 120: -240 degrees.
D). We’ve found our positive and negative coterminal angles, now let’s convert them to radians.(degrees x pi/180)
E). Positive: 8pi/3 and Negative: -4pi/3
EASY EASY EASYYYYYYYYYYY, BYE.
In trig they have many different types of graphing problems. I am going to teach you how to find all six trig functions. You are going to need to know that sin=y/r cos=x/r tan=y/x csc=r/y sec=r/x and cot=x/y. Now we can begin now that you know the formulas you will need to use.
ReplyDeleteEXAMPLE:
Find all six trig functions when given y=24 x=25
Well this is a triple so i know the other number is 7 but if you do not know then you will have to find the other number with Pythagorean and theorem.
sin=24/7 cos=25/7 tan=24/25 csc=7/24 sec=7/25 and cot=25/24.
This is the easiest way I can explain it if you dont get mrs. robinson can teach you.. she is a GREAT teacher :)
Graphing is essential in Advanced Math and is used for many different things. This past year we have learned many different ways to solve different problems which often included graphing. One of the first ways we learned to use graphing was when we learned trigonometry and using the inverse function. Here is an example of how to solve such a problem..
ReplyDeleteFind sin A in the triangle A where r=41 x=40
1. draw your coordinate plane and graph your triangle.
We know that that the sides of this triangle form a pythagorean triple; 9,40,41 therefore sine A is 9/41.
Graphing inverses are simple. here is an example..
triangle; a=2 b=2 c=sqrt16
tan=y/x= 2/2 = 1
1, because tan 1 is on our trig chart, we know that its inverse is 45.
2. 45 is in the first quadrant because it is less than 90 degrees.
3. if you wanted to move this angle you would make it neg. and add 180 for the 2nd quad. add 180 for the 3rd quad. and make it neg. and add 360 for 4th quad.
This comment has been removed by the author.
ReplyDeleteIn trig they have many different types of graphing problems, but I’m going teach you how to find all six trig functions.
ReplyDeleteThe six trig functions are: sin=y/r, cos=x/r, tan=y/x, csc=r/y, sec=r/x and cot=x/y
Example:
Find all six trig functions: given y=4 x= 3
This is a triple the answer is 5, but if you do not know then you will have to find the other number with Pythagorean and theorem. Now to find all the six functions
Sin=4/5
Cos=3/5
Tan= 4/3
Cot= ¾
Csc=5/4
Sec= 5/3
This is the simpliest thing ever if you know what your are doing and I got taught by the master of all math to learn how to do this and her name is Mrs. Robinson. Enjoy =)
In trig there are many graphs which all differ from one another, but in this particular graph I will show you have to find a reference point on the unit circle.
ReplyDeleteThe unit cirle is found on a coordinate plane and has specific points on the angles 90 degrees (0,1), 180 degrees (-1,0), 270 degrees (0,-1), and 360 degrees(1,0).
For Example:
Given Tan270 degrees
1.Go to 270 degrees on the unit circle and the points are (0,-1).
2. For tanget we know it is y/x, so you plug -1/0.
3. Divide -1/0 and you get 0.
4. So the answer is 0, which is a reference angle of tan 270 degrees.
** You could have also looked on your trig chart and just subtracted 180 from 270 until you got something with an absolute value 0 to 90 and looked on the trig chart.
I may have done this blog wrong but I tried to do soemthing different from everyone else.
Graphing Trig Functions
ReplyDeleteOur Equation
We want to graph the equation 8 cos(3x+π/2)-3. To do this, we’re first going to break it down into a formula with just variables in it. This equation will be Acos(Bx+C)-D.
Explanation of Variables
-Amplitude is half of the distance between the maximum and minimum values of the trigonometric curve.
-The vertical shift is the amount that the graph will move up or down from the original position of the graph.
-The period is the interval between each repetition of the function.
-The phase shift is the amount that a trigonometric graph shifts on its horizontal axis.
Calculate Variables
-Amplitude is the variable A in our equation, so our amplitude in this case will be 8.
-The vertical shift for our equation will be D in our variable equation, which equates to -3.
-The period will be 2π/B, or 2π/3.
-The phase shift is C/B, or π/6.
Graphing the Function
-When graphing the function, we know that it is a cosine trigonometric function.
-We also know that the height of the entire curve from the maximum to the minimum is 16, because our amplitude is 8, which is half of the entire height.
-Also, the graph will be shifted down 3 due to our vertical shift, telling us that our max is 5 and our min is -11.
-We know that our period is 2π/3, so if we divide this by 2, we get the halfway point being 2π/6, if we do the same thing again, we get our 25% point being π/6. Now, since we have the 25% point, we can add it to the halfway point, giving us 3π/6. We now have our five points as being 0, π/6, 2π/6, 3π/6, and 2π/3.
-We know that we need to shift our graph horizontally the right by π/6 radians.
-Now that we have the horizontal shift, we can add it to all of our 5 points and get our final X coordinates of the points. These are: π/6, 2π/6, 3π/6, 4π/6, and finally 5π/6.
-With our X coordinates of our critical points known, we can add the Y coordinates, giving us the final critical points of our cosine graph:
(π/6, 5)
(2π/6, 0)
(3π/6, -11)
(4π/6, -0)
(5π/6, 5)
-Our last step is to add the graph of cosine, crossing the X-axis at the specified critical points above, starting at (π/6, 5).
Okay so this will be my best holiday blog prompt because my wonderful big brother helped me!
This comment has been removed by the author.
ReplyDeleteGraphing Trig Functions
ReplyDeletesin430 degrees
1) Find the refrence angle of 430
430-360=70
2)Find what quadrant your answer is in
70 degrees is in the first quadrant
3)Find if sin is positive or negative
in quadrant one sin is positive. (sin=)
4)so sin=70 degrees
5) To find the positive coterminal to this I add 360 and I get 430. The negative coterminal is -290.