Q: Given $$\sin \theta = \frac{1}{2}$$, which equation would you use to solve for $$\theta$$?

$$\theta = \sin$$^{-1}$$\left(\frac{1}{2}\right)$$

Q: A medical imaging device uses the equation $$\sin \theta = 0.8 to $$determine the angle of a signal. What is the angle $$\theta (in $$degrees) that the device should use?

$$\theta = \sin$$^{-1}$$(0.8) \approx 53.1^\circ$$

Q: A sound engineer needs to find the angle at which a speaker should be placed so that the sine of the angle is $$0.6. $$Which equation should they use?

$$\theta = \sin$$^{-1}$$(0.6)$$

Q: A chemical reaction produces a signal with a sine ratio of $$0.3. $$What is the angle (in degrees) corresponding to this ratio?

$$\theta = \sin$$^{-1}$$(0.3) \approx 17.5^\circ$$

Question 1

Which of the following best describes the purpose of inverse trigonometric functions in precalculus?

Accepted Answer

They allow you to find an angle when you know a trigonometric ratio.

Question 2

Given $$\sin 	heta = \frac{1}{2}$$, which equation would you use to solve for $$	heta$$?

Accepted Answer

$$	heta = \sin$$^{-1}$$\left(\frac{1}{2}ight)$$

Question 3

If $$\sin 	heta = \frac{1}{2}$$, what is the principal value of $$	heta in $$radians?

Accepted Answer

$$\frac{\pi}{6}$$

Question 4

A medical imaging device uses the equation $$\sin 	heta = 0.8 to $$determine the angle of a signal. What is the angle $$	heta (in $$degrees) that the device should use?

Accepted Answer

$$	heta = \sin$$^{-1}$$(0.8) \approx 53.1^\circ$$

Question 5

Which of the following is the correct notation for the inverse sine function?

Accepted Answer

$$\sin$$^{-1}$$(x)$$

Question 6

A sound engineer needs to find the angle at which a speaker should be placed so that the sine of the angle is $$0.6. $$Which equation should they use?

Accepted Answer

$$	heta = \sin$$^{-1}$$(0.6)$$

Question 7

If $$\sin 	heta = -\frac{1}{2}$$, what is the principal value of $$	heta in $$radians?

Accepted Answer

$$-\frac{\pi}{6}$$

Question 8

Which of the following statements is true about inverse trigonometric functions?

Accepted Answer

They return the principal value, which is the main angle within a restricted range.

Question 9

A chemical reaction produces a signal with a sine ratio of $$0.3. $$What is the angle (in degrees) corresponding to this ratio?

Accepted Answer

$$	heta = \sin$$^{-1}$$(0.3) \approx 17.5^\circ$$

Question 10

If $$\sin 	heta = 1$$, what is the value of $$	heta in $$radians?

Accepted Answer

$$\frac{\pi}{2}$$

Inverse Trigonometric Functions: Introduction and Applications

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