Worksheet: Solving Equations by Using Inverse Trigonometric Functions

When we know the value of a trigonometric function of an angle, we can use the inverse to find the angle. This worksheet assesses your ability to solve equations by using inverse trigonometric functions.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

Given that , determine to the nearest tenth of a degree.

Q6:

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

Q7:

Find the angle to the nearest tenth of a degree, knowing that and .

Q8:

Find the set of values satisfying , where .

Q9:

Find the set of values satisfying , where .

Q10:

Find the set of values satisfying , where .

Q11:

Find the set of values satisfying given .

Q12:

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

Q13:

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

Q14:

Find the set of values satisfying given .

Q15:

Find the set of values satisfying given .

Q16:

Find the value of that satisfies where .

Q17:

Find the value of given where is the largest angle in the range .

Q18:

Find the smallest positive angle that satisfies both and .

Q19:

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