Q: If $$\sec \theta = \sin \theta \tan \theta$$, express $$\sec \theta as a $$single function of $$\theta.$$

$$\sin^2$ \theta / \cos \theta$$

Question 1

Which of the following graphs represents the function $$y = 	an x$$?

Accepted Answer

Graph (d)

Question 2

What is the domain of the cosine function $$y = \cos x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

Given $$y = 3 - 6 \sin\left(2x + \frac{\pi}{2}\right)$$, what is the amplitude of its graph?

Accepted Answer

$$6$$

Question 4

If $$\cos 	heta = \frac{3}{5}$$ and $$	heta is in $$quadrant IV, what is $$\sin 	heta$$?

Accepted Answer

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

Question 5

What is the period of the function $$y = 3 - 6 \sin\left(2x + \frac{\pi}{2}\right)$$?

Accepted Answer

$$\pi$$

Question 6

A central angle of a circle with radius $$150 cm $$intercepts an arc of $$200 cm. $$What is the radian measure of the angle?

Accepted Answer

$$\frac{4}{3}$$ radians

Question 7

What is the range of the secant function $$y = \sec x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 8

The position of a weight attached to a spring is given by $$s(t) = -4 \cos 8\pi t. $$What is the period of the motion?

Accepted Answer

$$\frac{1}{4}$$

Question 9

Suppose point $$P is on a $$circle with radius $$60 cm$$, and $$OP is $$rotating with angular speed $$\frac{\pi}{12}$$ radians per second. What is the linear speed of $$P$$?

Accepted Answer

$$5 cm/sec$$

Question 10

Given $$y = -2 - \cot\left(x - \frac{\pi}{2}\right)$$, what is the vertical translation of the graph?

Accepted Answer

Down 2 units

Question 11

If $$\sec 	heta = \sin 	heta 	an 	heta$$, express $$\sec 	heta as a $$single function of $$	heta.$$

Accepted Answer

$$\sin^2$ 	heta / \cos 	heta$$

Question 12

The average monthly temperature in San Antonio, Texas, is modeled by $$f(x) = 16.5 \sin\left[\frac{2\pi}{12}(x-4)\right] + 68.5. $$What is the amplitude of this function?

Accepted Answer

$$16.5$$

Question 13

What is the least positive value for which the tangent function is undefined?

Accepted Answer

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

Question 14

A Ferris wheel has a radius of $$30.0 ft. $$How far is the person above the ground after the wheel turns $$\frac{\pi}{2}$$ radians, assuming the lowest point is at ground level?

Accepted Answer

$$60 ft$$

Question 15

Express $$	an^2$ x - \sec^2$ x in $$terms of $$\sin x$$ and $$\cos x$$, and simplify.

Accepted Answer

$$-1$$

Question 16

If $$y = -\csc 2x$$, what is the period of the function?

Accepted Answer

$$\pi$$

Question 17

A car's gasoline gauge arrow is $$4\frac{1}{2} in. $$long. Through what angle does the arrow rotate when it moves $$1 in. on $$the gauge?

Accepted Answer

$$\frac{1}{4.5}$$ radians

Question 18

Given $$y = 3 \csc \pi x$$, what is the period of the function?

Accepted Answer

$$1$$

Question 19

If $$\cos 	heta = \frac{3}{5}$$ and $$	heta is in $$quadrant IV, what is $$	an 	heta$$?

Accepted Answer

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

Question 20

The position of a weight attached to a spring is $$s(t) = -4 \cos 8\pi t. $$What is the maximum height above equilibrium?

Accepted Answer

$$4$$ inches

Trigonometry Study Guide: Circular Functions, Graphs, and Applications

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