# Worksheet: Inverse Trigonometric Functions

In this worksheet, we will practice calculating exact values of trigonometric inverses and recognizing the inverse of trigonometric functions from tables.

Q1:

The given tables show some values of , , and . Which function corresponds to the function ?

 𝑥 𝑓(𝑥) −√32 −12 0 12 √22 −𝜋3 −𝜋6 0 𝜋4 𝜋3
 𝑥 𝑔(𝑥) −√32 −√22 0 √32 1 −𝜋6 −𝜋4 0 𝜋6 𝜋2
 𝑥 ℎ(𝑥) −1 −12 0 √22 √32 −𝜋2 −𝜋6 0 𝜋4 𝜋3
• A
• B
• C

Q2:

The given tables show some values of , , and . Which function corresponds to the function ?

 𝑥 𝑓(𝑥) −√3 −1 0 1√3 1 −𝜋3 −𝜋4 0 𝜋6 𝜋4
 𝑥 𝑔(𝑥) −√3 −12 0 √3 1 −𝜋6 −𝜋4 0 𝜋6 𝜋2
 𝑥 ℎ(𝑥) −1 −12 0 1√3 √3 −𝜋4 −𝜋6 0 𝜋6 𝜋3
• A
• B
• C

Q3:

Find the exact value of .

• A
• B
• C
• D
• E

Q4:

Find the exact value of , in radians in terms of , which is located in the 1st quadrant.

• A1
• B
• C
• D
• E0

Q5:

Find the exact value of in radians.

Q6:

Which of these two value tables shows a domain of the sine function that can be used to construct its inverse function?

Table A

 𝑥 sin𝑥 0 𝜋6 𝜋4 𝜋3 𝜋2 2𝜋3 3𝜋4 5𝜋6 𝜋 0 12 √22 √32 1 √32 √22 12 0

Table B

 𝑥 sin𝑥 −𝜋2 −𝜋3 −𝜋4 −𝜋6 0 𝜋6 𝜋4 𝜋3 𝜋2 −1 −√32 −√22 −12 0 12 √22 √32 1
• ATable A
• BTable B

Q7:

Which of these two value tables shows a domain of the cosine function that can be used to construct its inverse function?

Table A

 𝑥 cos𝑥 0 𝜋6 𝜋4 𝜋3 𝜋2 2𝜋3 3𝜋4 5𝜋6 𝜋 1 √32 √22 12 0 −12 −√22 −√32 −1

Table B

 𝑥 cos𝑥 −𝜋2 −𝜋3 −𝜋4 −𝜋6 0 𝜋6 𝜋4 𝜋3 𝜋2 0 12 √22 √32 1 √32 √22 12 0
• ATable B
• BTable A

Q8:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q9:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q10:

Find the exact value of in radians.

• A
• B
• C
• D

Q11:

Find the exact value of .

• A
• B
• C
• D
• E

Q12:

Which of the following is closest to ?

• A
• B
• C
• D
• E

Q13:

Find the exact value of in radians.

• A
• B
• C
• D

Q14:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q15:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q16:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q17:

is a triangle where and . Find the value of giving the answer to the nearest minute.

• A
• B
• C
• D

Q18:

Find the exact value of , in radians in terms of , which is located in the 1st quadrant.

• A
• B
• C
• D
• E

Q19:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q20:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q21:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q22:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q23:

Find the exact value of in radians.

• A
• B
• C
• D0
• E

Q24:

Find the exact value of in radians.

Q25:

Find the exact value of in radians.

• A
• B
• C
• D0
• E