Question 1

What is the y-intercept of the function $$y = \sec x$$?

Accepted Answer

$$1$$

Question 2

Given the function $$y = -\frac{1}{2} \sin(4x + 3\pi)$$, what is the amplitude?

Accepted Answer

$$\frac{1}{2}$$

Question 3

Given the function $$y = -\frac{1}{2} \sin(4x + 3\pi)$$, what is the period?

Accepted Answer

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

Question 4

Given the function $$y = -\frac{1}{2} \sin(4x + 3\pi)$$, what is the phase shift?

Accepted Answer

$$-\frac{3\pi}{4}$$

Question 5

An experiment in a wind tunnel generates cyclic waves. The wind speed $$V (in ft/s) at $$time $$t (in $$seconds) is modeled by $$V = 22 \sin\left(\frac{\pi}{16} t - \frac{\pi}{2}\right) + 38. $$What is the maximum wind speed recorded?

Accepted Answer

$$60 ft/s$$

Question 6

For what value(s) of $$x in$$ $$0 \u003c x \u003c 2\pi$$ does $$\cos x = -1$$?

Accepted Answer

$$x = \pi$$

Question 7

For what value(s) of $$x in$$ $$0 \u003c x \u003c 2\pi$$ does $$\sin x = 1$$?

Accepted Answer

$$x = \frac{\pi}{2}$$

Question 8

Evaluate $$\frac{	an 80^\circ - \sin 80^\circ}{\cos 80^\circ}$$ without a calculator.

Accepted Answer

$$0$$

Question 9

If $$\sin 	heta = \frac{5}{3}$$ and $$\cos 	heta = \frac{2}{3}$$, what is $$	an 	heta$$?

Accepted Answer

$$\frac{5}{2}$$

Question 10

Find the exact value of $$\sin 330^\circ \sin 270^\circ.$$

Accepted Answer

$$\frac{1}{2}$$

Question 11

Find the exact value of $$	an 150^\circ \cos 210^\circ.$$

Accepted Answer

$$-\frac{5}{3}$$

Question 12

Find the inverse function $$f^{-1} of$$ $$f(x) = 2 \sin x - 4.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{\$$sin^{-1} x + 4$$}{2}$$

Question 13

Find the exact value of $$\sin$$^{-1}$$(\sin \frac{4\pi}{5}).$$

Accepted Answer

$$\pi - \frac{4\pi}{5}$$

Question 14

Solve for $$x$$: $$8 \sin$$^{-1}$$ x - 4\pi = 6 \sin$$^{-1}$$ x - 5\pi.$$

Accepted Answer

$$x = -1$$

Question 15

Convert $$160^\circ to $$radians. Express the answer as a multiple of $$\pi.$$

Accepted Answer

$$\frac{8\pi}{9}$$

Question 16

Convert $$7$$ radians to degrees. Express the answer in decimal form, rounded to two decimal places.

Accepted Answer

$$401.07^\circ$$

Question 17

If a sector of a circle has a central angle of $$120^\circ$$ and an area of $$30$$ square meters, what is the radius $$r$$? (Round to two decimal places if necessary.)

Accepted Answer

$$5.35 m$$

Question 18

An object travels around a circle of radius $$10 cm. In$$ $$20$$ seconds, a central angle of $$\frac{1}{3}$$ radian is swept out. What is the linear speed of the object?

Accepted Answer

$$\frac{1}{6} cm/sec$$

Question 19

If the length of an arc is $$13.68$$ meters and the central angle is $$3.6$$ radians, what is the radius $$r$$?

Accepted Answer

$$3.8 m$$

MTH 162 Test 1 Study Guide – Trigonometric Functions, Graphs, and Applications

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