# Lesson Worksheet: Solving Equations Using Inverse Trigonometric Functions Mathematics

In this worksheet, we will practice solving equations by using inverse trigonometric functions in the first quadrant.

Q1:

If is an acute angle, find given . Give the answer to the nearest second.

• A
• B
• C

Q2:

Find, to the nearest tenth of a degree, the measure of the angle of .

• A
• B
• C
• D
• E

Q3:

Given that is an acute angle and that , determine to the nearest tenth of a degree.

Q4:

Find given and is an acute angle. Give the answer to the nearest second.

• A
• B
• C

Q5:

Find the smallest positive angle that satisfies both and .

Q6:

Find the value of given that is an acute angle and . Give the answer to the nearest second.

• A
• B
• C

Q7:

Find the measure of in degrees given where is an acute angle.

Q8:

Find the measure of given where . Give the answer to the nearest second.

• A
• B
• C
• D

Q9:

Find the measure of in degrees given where is an acute angle.

Q10:

Solve .

• A
• B
• C
• D
• E

Q11:

Solve .

• A
• B
• C
• D

Q12:

Find the value of given where is an acute angle.

Q13:

Find the value of without using a calculator, given where is an acute angle.

• A
• B2
• C
• D
• E1

Q14:

Find the value of without using a calculator, given where is an acute angle.

• A
• B1
• C2
• D0

Q15:

Find the value of without using a calculator, given where is an acute angle.

• A
• B
• C
• D
• E3

Q16:

Given that is an acute angle and , determine the value of in radians.

• A
• B
• C
• D
• E

Q17:

If the angle is in the standard position, , and , is it possible for to measure ?

• AYes
• BNo

Q18:

Fill in the blank: Given that is an acute angle, if and , then .

• A
• B
• C
• D
• E

Q19:

Find the value of that satisfies the equation . Round your answer to two decimal places.

Q20:

Find the value of that satisfies the equation .

Q21:

Given that is an acute angle, find the value of that satisfies the equation . Round your answer to two decimal places.

Q22:

True or False: The acute angle that satisfies is .

• AFalse
• BTrue

Q23:

True or False: The smallest positive angle that satisfies is .

• ATrue
• BFalse

Q24:

Find the acute angle that satisfies . Round your answer to two decimal places.

Q25:

If , find to the nearest second.

• A
• B
• C
• D
• E