MAT 123Name
Johns
Inverse Trig Functions I
1. a) On both the unit circle and the sin x graph, draw points corresponding to the solutions to the equation sin x = 0.8.
Now use the inverse sine button on your calculator to find one solution to sin x =0.8. Be sure you are in radian mode.
Write down the answer to 3 decimal places and which quadrant the angle is in.x ≈ in Quadrant
Now locate your answer on the graph. Label this point A.
Now locate your answer on the unit circle. Label this point A. Also draw in the angle from standard position.
b) On both the unit circle and the graph above, now indicatelocations for the solutions to sin x =.
Use your calculator to find one solution to sin x =. Write down the answer to 3 dp and the quadrant.
x ≈ in Quadrant
Now locate your answer on the graph. Label this point B.
Now locate your answer on the unit circle. Label this point B. Also draw in the angle from SP.
c) Use your calculator in radian mode to get answers to 3dp for the following equations.
sin x = 1x ≈sin x = −1x ≈sin x = 0x ≈
For each answer, locate (but do not label) where your solution is on the unit circle and the graph.
d) Your calculator does not give all the solutions to each equation above – only one solution. In what two quadrants do most of the solutions lie?
Inverse sine function returns mostly angles in Quadrants and
The angles that the inverse sine function returns fall between what two special angles in radians? Use interval notation.
Inverse sine functionreturns angles
e) On the unit circle and graph below, shade out the quadrants where the inverse sine function does NOT return answers.
We know that y = sin x does not have an inverse function. But does the unshaded portion of the graph below have an inverse
function?
2. a) On both the unit circle and the cos x graph, draw points corresponding to the solutions to the equation cos x = .
What solution does the inverse cosine button on your calculator give for cos x = ?
Write down the answer to 3 decimal places and which quadrant the angle is in.x ≈ in Quadrant
Now locate your answer on the graph. Label this point A.
Now locate your answer on the unit circle. Label this point A. Also draw in the angle from SP.
b) On both the unit circle and the graph above, indicate the solutions to cos x = −0.5.
Use your calculator to find one solution to cos x = −0.5. Write down the answer to 3 dp and the quadrant.
x ≈ in Quadrant
The angle the calculator gives you is a special angle. What is the solution exactly?x =
Now locate your answer on the graph. Label this point B.
Now locate your answer on the unit circle. Label this point B. Also draw in the angle from SP.
c) Use your calculator in radian mode to get answers to 3dp for the following equations.
cos x = 1x ≈cosx = −1x ≈cos x = 0x ≈
For each answer, locate (but do not label) where your solution is on the unit circle and the graph.
d) Your calculator does not give all the solutions for each equation above – only one solution. In what two quadrants do most of the solutions lie?
Inverse cosine function returns mostly angles in Quadrants and
The angles that the inverse cosine function returns fall between what two special angles in radians? Use interval notation.
Inverse cosine functionreturns angles
e) On the unit circle and graph below, shade out the quadrants where the inverse cosine function does NOT return answers.
We know that y = cos x does not have an inverse function. But does the unshaded portion of the graph below have an inverse
function?
3. a) On both the unit circle and the tan x graph, draw points corresponding to the solutions to the equation tan x = 2.
What solution does the inverse cosine button on your calculator give for tan x = 2.
Write down the answer to 3 decimal places and which quadrant the angle is in.x ≈ in Quadrant
Now locate your answer on the graph. Label this point A.
Now locate your answer on the unit circle. Label this point A. Also draw in the angle from SP.
b) On both the unit circle and the graph above, indicate the solutions to tan x = −1.
Use your calculator to find one solution to tan x = −1. Write down the answer to 3 dp and the quadrant.
x ≈ in Quadrant
The angle the calculator gives you is a special angle. What is the solution exactly?x =
Now locate your answer on the graph. Label this point B.
Now locate your answer on the unit circle. Label this point B. Also draw in the angle from SP.
c) Use your calculator in radian mode to get answers to 3dp for the following equations.
tan x =x ≈tan x = 0x ≈tan x = −4x ≈
For each answer, locate (but do not label) where your solution is on the unit circle and the graph.
d) Your calculator does not give all the solutions for each equation above – only one solution. In what two quadrants do most of the solutions lie?
Inverse tangent function returns mostly angles in Quadrants and
The angles that the inverse tangent function returns fall between what two special angles in radians? Use interval notation.
Inverse tangent functionreturns angles
e) On the unit circle and graph below, shade out the quadrants where the inverse tangent function does NOT return answers.
We know that y = tan x does not have an inverse function. But does the unshaded portion of the graph below have an inverse
function?
4. Below is the graph of y = sin x, restricted to the angles that the inverse sine function returns. In what quadrants are these angles?
On the same axes, sketch the inverse sine function y = sin-1 x.
State the domain and range of y = sin-1 x using interval notation.
D: x
R: y
What are the exact coordinates of the right endpoint of
the graph of y = arcsin x?
()
4. Below is the graph of y = cos x, restricted to the angles that the inverse cosine function returns. In what quadrants are these angles?
On the same axes, sketch the inverse cosine function
y = cos-1 x.
State the domain and range of y = cos-1 x using interval notation.
D: x
R: y
What is the y intercept of y = arccos x?
()
4. Below is the graph of y = tan x, restricted to the angles that the inverse tangent function returns. In what quadrants are these angles?
On the same axes, sketch the inverse tangent function
y = tan-1 x.
State the domain and range of y = tan-1 x using interval notation.
D: x
R: y
What are the equations of the two horizontal asymptotes of
y = arctan x?
x =