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

$$\sin \theta = \frac{1}{\csc \theta}$$

$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$

Question 1

Which of the following best describes a coterminal angle to $$-150^\circ$$ with the least positive measure?

Accepted Answer

$$210^\circ$$

Question 2

A wheel rotates at 270 revolutions per minute. Through how many degrees does a point on the edge move in 5 seconds?

Accepted Answer

$$81000^\circ$$

Question 3

Given that the terminal side of an angle in standard position passes through the point $$(8, -6)$$, what is the value of $$	an 	heta$$?

Accepted Answer

$$-\frac{6}{8}$$

Question 4

If two angles are complementary, which equation must be true for their measures $$x$$ and $$y$$?

Accepted Answer

$$x + y = 90^\circ$$

Question 5

Convert $$105^\circ 20' 32'' to $$decimal degrees to the nearest thousandth.

Accepted Answer

$$105.342^\circ$$

Question 6

Which trigonometric function is undefined for an angle whose terminal side lies on the positive $$y-$$axis?

Accepted Answer

$$\cot 	heta$$

Question 7

Given that $$\sin 	heta = \frac{5}{13}$$ and $$	heta is in $$Quadrant I, what is $$\cos 	heta$$?

Accepted Answer

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

Question 8

If triangle $$ABC is $$similar to triangle $$DEF$$, which of the following must be true?

Accepted Answer

Corresponding angles are equal and corresponding sides are proportional.

Question 9

Joey is 63 inches tall and casts a 42-inch shadow. At the same time, a tree casts a 38-foot shadow. What is the height of the tree in feet?

Accepted Answer

$$57 ft$$

Question 10

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 11

If $$\cot 	heta = -2$$ and $$	heta is in $$Quadrant II, what is the sign of $$\sin 	heta$$?

Accepted Answer

Positive

Question 12

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

Accepted Answer

$$\sin 	heta = \frac{1}{\csc 	heta}$$

Question 13

Given that $$	an 	heta \u003e 0$$ and $$\csc 	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant III

Question 14

If $$\cos 	heta = -1.7$$, is this value possible for any real angle $$	heta$$?

Accepted Answer

Impossible

Question 15

What is the range of the sine function?

Accepted Answer

$$[-1, 1]$$

Question 16

If the terminal side of an angle in standard position passes through $$(0, -5)$$, what is $$\sin 	heta$$?

Accepted Answer

$$-1$$

Question 17

Given that $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 18

Which of the following is the quotient identity for $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{\sin 	heta}{\cos 	heta}$$

Question 19

A triangle has angles measuring $$33^\circ$$ and $$26^\circ. $$What is the measure of the third angle?

Accepted Answer

$$121^\circ$$

Angles, Triangles, and Trigonometric Functions: Structured Study Notes

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