$$8 \times \frac{\pi}{4} = 2\pi cm$$

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

$$\theta = 0, \pi, \frac{\pi}{3}, \frac{5\pi}{3}$$

$$\sec \theta = \frac{1}{\cos \theta}$$

Question 1

Convert $$120^{\circ} to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 2

A circle has a radius of $$8 cm. $$What is the length of the arc subtended by a central angle of $$\frac{\pi}{4}$$ radians?

Accepted Answer

$$8 	imes \frac{\pi}{4} = 2\pi cm$$

Question 3

Which of the following is the correct value for $$\sin\left(\frac{\pi}{6}\right)$$?

Accepted Answer

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

Question 4

Find the least positive coterminal angle for $$-\frac{\pi}{3}.$$

Accepted Answer

$$\frac{5\pi}{3}$$

Question 5

Given $$\cos 	heta = -\frac{3}{5}$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 6

Which trigonometric function is positive in the third quadrant?

Accepted Answer

$$	an 	heta$$

Question 7

If $$	an 	heta = \frac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

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

Question 8

Which of the following is a Pythagorean identity?

Accepted Answer

$$\sin^2$ 	heta + \cos^2$ 	heta = 1$$

Question 9

Evaluate $$\cos(2x) if$$ $$\sin x = \frac{3}{5}$$ and $$x is in $$the first quadrant.

Accepted Answer

$$\frac{7}{25}$$

Question 10

Solve for $$	heta in$$ $$[0, 2\pi)$$: $$2\cos^2$ 	heta - 1 + \cos 	heta = 0.$$

Accepted Answer

$$	heta = 0, \pi, \frac{\pi}{3}, \frac{5\pi}{3}$$

Question 11

Which of the following is the correct double-angle formula for $$\sin 2x$$?

Accepted Answer

$$2\sin x \cos x$$

Question 12

If $$\sin^2$ 	heta = \frac{3}{4}$$ and $$	heta is in $$the second quadrant, what is $$\cos 	heta$$?

Accepted Answer

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

Question 13

Which of the following is the reciprocal identity for $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 14

A Ferris wheel has a radius of $$15$$ meters. What is the length of the arc corresponding to a central angle of $$60^{\circ}$$?

Accepted Answer

$$5\pi$$ meters

Question 15

Which of the following is the correct half-angle formula for $$\sin^2$ x$$?

Accepted Answer

$$\sin^2$ x = \frac{1}{2}(1 - \cos 2x)$$

Trigonometric Functions and Their Applications in Calculus

Study Guide - Practice Questions