Q: Which of the following statements is always true for all real $$\theta$$?

$$\tan^2$\theta + 1 = \sec^2$\theta$$

Question 1

If an angle $$	heta in $$standard position is between $$\frac{7\pi}{2}$$ and $$4\pi$$, in which quadrant does the terminal side of $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 2

Which of the following statements is always true for all real $$	heta$$?

Accepted Answer

$$	an^2$	heta + 1 = \sec^2$	heta$$

Question 3

Find the least positive angle coterminal with $$411^\circ.$$

Accepted Answer

$$51^\circ$$

Question 4

A circle has a radius of 20 inches and subtends a central angle of $$\frac{4\pi}{5}$$ radians. What is the exact length of the arc?

Accepted Answer

$$16\pi$$ inches

Question 5

If a wheel rolls a distance of 50 inches as it turns through an angle of $$207^\circ$$, what is the radius of the wheel? (Round your answer to two decimal places.)

Accepted Answer

13.84 inches

Question 6

Convert $$\frac{17\pi}{12}$$ radians into degrees.

Accepted Answer

$$255^\circ$$

Question 7

Given the point $$(13, -223) is on $$the terminal side of angle $$	heta in $$standard position, what is $$\sin	heta$$?

Accepted Answer

$$-\frac{223}{324}$$

Question 8

What is the exact value of $$\cos\left(\frac{3\pi}{4}\right)$$?

Accepted Answer

$$-\frac{\sqrt{2}}{2}$$

Question 9

Estimate $$\csc 41^\circ to $$two decimal places using your calculator.

Accepted Answer

1.52

Question 10

What is the domain and range of the cosine function $$y = \cos x in $$interval notation?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-1, 1]$$

Question 11

If $$\sin	heta \u003e 0$$ and $$\cos	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant II

Question 12

If the point $$(-4, -1) is on $$the terminal side of angle $$	heta in $$standard position, what is $$	an	heta$$?

Accepted Answer

Question 13

If $$\sin	heta = -\frac{1}{3}$$ and $$	an	heta \u003c 0$$, what is $$\cos	heta$$?

Accepted Answer

$$\frac{2\sqrt{2}}{3}$$

Question 14

If $$\sin	heta = 45$$, what is $$\sin(-	heta)$$?

Accepted Answer

$$-45$$

Question 15

What is the amplitude and period of $$y = 2\cos x + 1$$?

Accepted Answer

Amplitude: 2, Period: $$2\pi$$

Question 16

What is the amplitude and period of $$y = \sin\frac{x}{2} - 3$$?

Accepted Answer

Amplitude: 1, Period: $$4\pi$$

Question 17

For the function $$y = -\cos\left(x + \frac{\pi}{6}\right) + 1$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: 1, Period: $$2\pi$$, Phase shift: $$-\frac{\pi}{6}$$

Question 18

A Ferris wheel with a radius of 20 meters makes one full revolution every $$4\pi$$ seconds. What is the angular speed of the wheel in radians per second?

Accepted Answer

$$\frac{\pi}{2}$$ radians/second

Question 19

If $$	an	heta \u003e 0$$ and $$\csc	heta \u003e 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant I

Precalculus Exam 1 Review – Step-by-Step Guidance

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