Q: Which of the following is the correct reciprocal identity for $$\sec \theta$$?

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

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side lies along the positive x-axis.

Question 2

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^\circ$$

Question 3

A circle has a radius of 10 meters. What is the length of the arc intercepted by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

$$\frac{10\pi}{3}$$ meters

Question 4

Which of the following is the correct formula for the linear speed $$v of a $$point moving in a circle of radius $$r$$ with angular speed $$\omega$$?

Accepted Answer

$$v = r\omega$$

Question 5

If the sine of an angle $$	heta is$$ $$\frac{3}{5}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 6

Find the period of the function $$y = \sin(2x).$$

Accepted Answer

$$\pi$$

Question 7

Which of the following angles is coterminal with $$-135^\circ$$?

Accepted Answer

$$225^\circ$$

Question 8

A ferris wheel has a radius of 20 feet and rotates at 4 revolutions per minute. What is the linear speed, in feet per minute, of a point on the edge?

Accepted Answer

$$160\pi$$

Question 9

Which of the following is the amplitude of $$y = 3\cos(x)$$?

Accepted Answer

$$3$$

Question 10

If $$	an 	heta = -2$$ and $$\sin 	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 11

Find the exact value of $$\sin 45^\circ.$$

Accepted Answer

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

Question 12

Which of the following is the correct definition of a radian?

Accepted Answer

The measure of a central angle that intercepts an arc equal in length to the radius of the circle.

Question 13

What is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 14

If $$\sin 	heta = -\frac{5}{13}$$ and $$	heta is in $$quadrant III, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 15

Which of the following is the period of $$y = 	an(x)$$?

Accepted Answer

$$\pi$$

Question 16

A police helicopter is flying at 800 feet. A stolen car is sighted at an angle of depression of $$72^\circ. $$What is the horizontal distance from the helicopter to the car (to the nearest foot)?

Accepted Answer

$$254$$ feet

Question 17

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

Accepted Answer

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

Question 18

Find the complement of a $$37^\circ$$ angle.

Accepted Answer

$$53^\circ$$

Question 19

If $$\sin 	heta = \frac{4}{5}$$ and $$	heta is in $$quadrant I, what is $$	an 	heta$$?

Accepted Answer

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

Question 20

Which of the following describes the effect of the coefficient $$A in$$ $$y = A\sin(x)$$?

Accepted Answer

It changes the amplitude of the sine curve.

Chapter 4: Trigonometric Functions – Comprehensive Study Notes

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