Question 1

A circular track has a radius of 100 meters. How long is the arc subtended by a central angle of $$72^\circ$$? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$125.6$$ meters

Question 2

Convert $$225^\circ to $$radians.

Accepted Answer

$$\dfrac{5\pi}{4}$$

Question 3

Which of the following angles is coterminal with $$-30^\circ$$?

Accepted Answer

$$330^\circ$$

Question 4

Find the exact value of $$\sin\left(\dfrac{5\pi}{6}\right).$$

Accepted Answer

$$\dfrac{1}{2}$$

Question 5

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

Tangent and cotangent

Question 6

Given $$\sin(	heta) = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, find $$\cos(	heta).$$

Accepted Answer

$$-\dfrac{4}{5}$$

Question 7

A ladder leans against a wall, forming a $$65^\circ$$ angle with the ground. If the foot of the ladder is $$5$$ feet from the wall, how long is the ladder (to the nearest tenth)?

Accepted Answer

$$11.0 ft$$

Question 8

Which of the following is the period of the function $$y = 2 \sin\left(3x\right)$$?

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 9

Simplify $$\dfrac{1 - \cos^2$(x)}{\sin(x)}$$ using trigonometric identities.

Accepted Answer

$$\sin(x)$$

Question 10

Solve for $$x in$$ $$2\sin(x) - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}$$

Question 11

If $$y = 3\cos\left(2x - \dfrac{\pi}{2}\right) + 1$$, what is the vertical shift?

Accepted Answer

$$1$$

Question 12

Find the reference angle for $$210^\circ.$$

Accepted Answer

$$30^\circ$$

Question 13

Evaluate $$\arccos\left(-\dfrac{1}{2}\right) in $$radians.

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 14

Which equation represents a sine function with amplitude $$4$$, period $$\pi$$, and midline $$y = -2$$?

Accepted Answer

$$y = 4\sin(2x) - 2$$

Question 15

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos(x)$$

Question 16

If $$	an(	heta) = -1$$ and $$	heta is in $$Quadrant II, what is $$	heta$$?

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 17

Which identity is used to verify $$1 + 	an^2$(x) = \sec^2$(x)$$?

Accepted Answer

Pythagorean Identity

Question 18

Solve for $$x in$$ $$\cos(2x) = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}$$

Question 19

A Ferris wheel with a radius of $$20$$ meters makes one full revolution every $$40$$ seconds. If a rider starts at the lowest point, which equation models the rider's height $$h (in $$meters) above the ground after $$t$$ seconds, assuming the center is $$22$$ meters above the ground?

Accepted Answer

$$h = 22 + 20\sin\left(\dfrac{\pi}{20}t - \dfrac{\pi}{2}\right)$$

Question 20

Which of the following is the solution to $$2\sin^2$(x) - 1 = 0$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = \dfrac{\pi}{2}, \dfrac{3\pi}{2}$$

Comprehensive Study Guide: Trigonometric Functions, Identities, and Equations

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