# Lesson Worksheet: Inverse Trigonometric Functions Mathematics • 10th Grade

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:

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

Q4:

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

Q5:

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

• A
• B
• C
• D

Q6:

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

 𝑥 𝑓(𝑥) −1 −12 0 12 √22 𝜋 𝜋4 𝜋2 𝜋3 −𝜋4
 𝑥 𝑔(𝑥) −√32 −√22 0 √32 1 5𝜋6 3𝜋4 𝜋2 𝜋6 0
 𝑥 ℎ(𝑥) −1 −12 0 √32 1 𝜋2 3𝜋4 𝜋 𝜋3 0
• A
• B
• C

Q7:

True or False: If , then .

• ATrue
• BFalse

Q8:

True or False: .

• ATrue
• BFalse

Q9:

Find the exact value of .

Q10:

Complete the following: , where .

This lesson includes 11 additional questions and 91 additional question variations for subscribers.