Q: Which of the following is a fundamental trigonometric identity?

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

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 coincides with the positive x-axis.

Question 2

Convert $$135^	ext{o} to $$radians.

Accepted Answer

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

Question 3

A camera lens has a viewing angle of $$6^	ext{o}9'$$ and is 725 feet from an object. What is the approximate field width imaged by the lens? (Use $$	heta \approx 0.107$$ radians)

Accepted Answer

$$77.6$$ feet

Question 4

Find the length of the arc of a circle of radius $$4$$ meters subtended by a central angle of $$0.75$$ radians.

Accepted Answer

$$3$$ meters

Question 5

What is the area of a sector of a circle of radius $$3$$ meters formed by an angle of $$45^	ext{o}$$? (Round to two decimal places)

Accepted Answer

$$3.54 m$^2$$

Question 6

A child spins a rock at the end of a $$2-$$foot rope at $$180$$ revolutions per minute. What is the linear speed of the rock when released?

Accepted Answer

$$2262 ft/$$min

Question 7

Given $$\sin 	heta = \frac{2}{5}$$ and $$	heta is $$acute, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{\sqrt{21}}{5}$$

Question 8

Which of the following is a fundamental trigonometric identity?

Accepted Answer

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

Question 9

If $$\sin 	heta  0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 10

What is the period of the function $$y = 5 \sin(3x)$$?

Accepted Answer

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

Question 11

Which trigonometric function is even?

Accepted Answer

Cosine

Question 12

What is the amplitude of $$y = -2 \sin(2x)$$?

Accepted Answer

$$2$$

Question 13

Which of the following is the reciprocal of $$\sin 	heta$$?

Accepted Answer

$$\csc 	heta$$

Question 14

If $$\sin 	heta = \frac{3}{5}$$ and $$\cos 	heta = -\frac{4}{5}$$, what is $$	an 	heta$$?

Accepted Answer

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

Question 15

What is the domain of the tangent function $$y = 	an x$$?

Accepted Answer

All real numbers except odd multiples of $$\frac{\pi}{2}$$

Question 16

Given the unit circle, what is $$\sin 60^	ext{o}$$?

Accepted Answer

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

Question 17

Which equation expresses the period $$T of$$ $$y = A \sin(\omega x)$$?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Question 18

If $$y = 2 \csc x - 1$$, what is the range of the function?

Accepted Answer

$$(-\infty, -3] \cup [1, \infty)$$

Question 19

A sinusoidal function modeling daylight hours in Boston is $$y = 3.105 \sin\left(\frac{2\pi}{365}x - \frac{323\pi}{730}\right) + 12.175. $$What is the amplitude?

Accepted Answer

$$3.105$$

Question 20

Which property is true for the sine function?

Accepted Answer

It is an odd function.

Trigonometric Functions: Angles, Right Triangles, and the Unit Circle

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