Unit 5 · Test

Unit 5 test: Inverse Trigonometric Functions

15 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This test covers the definitions, domains and ranges of the inverse sine, cosine and tangent functions, evaluating them exactly and with a calculator, and compositions of trig functions with their inverses.

Question 1

What is the range of $y = \arccos x$ ?

Question 2

Which expression is undefined?

Question 3

In a right triangle, the side adjacent to angle $\theta$ is $8$ and the hypotenuse is $15$ . Find $\theta$ to the nearest tenth of a degree.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

A road rises $3$ meters for every $40$ meters of horizontal distance. What angle does the road make with the horizontal, to the nearest tenth of a degree?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

Find the exact value of $\arcsin(-1)$ in radians.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

Find the exact value of $\arccos\dfrac{\sqrt{2}}{2}$ in radians.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Find the exact value of $\arctan\left(-\sqrt{3}\right)$ in radians.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

Find $\arccos\left(-\dfrac{\sqrt{3}}{2}\right)$ in degrees.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

Use a calculator to find $\arcsin 0.62$ in radians, rounded to the nearest hundredth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

Find the exact value of $\arcsin\left(\sin\dfrac{2\pi}{3}\right)$ in radians.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

Find the exact value of $\arctan\left(\tan\dfrac{5\pi}{4}\right)$ in radians.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

Find the exact value of $\sin\left(\arccos\dfrac{3}{5}\right)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Find the exact value of $\tan\left(\arcsin\left(-\dfrac{8}{17}\right)\right)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 14

Find the exact value of $\cos\left(\arcsin\left(-\dfrac{1}{3}\right)\right)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

For $x > 0$ , which expression equals $\sin(\arctan x)$ ?