$$\tan \theta = \frac{1}{\cot \theta}$$

$$\theta' = 180^\\circ - \theta$$

Multiply by $$\frac{180^\\circ}{\pi}$$

Question 1

Which of the following best describes a ray in geometry?

Accepted Answer

A part of a line with only one endpoint and extends forever in one direction.

Question 2

Convert $$135^\circ to $$radians.

Accepted Answer

$$\frac{135\pi}{180} = \frac{3\pi}{4}$$ radians

Question 3

What is the radian measure of an angle whose intercepted arc is equal to the radius of the circle?

Accepted Answer

$$1$$ radian

Question 4

If $$\sin 	heta = \frac{\sqrt{3}}{2}$$ and $$	heta is in $$the interval $$[0, \pi]$$, what is $$	heta$$?

Accepted Answer

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

Question 5

Which of the following is the correct definition of $$\sin t in $$terms of the unit circle?

Accepted Answer

$$\sin t = y$$

Question 6

What is the period of the sine and cosine functions?

Accepted Answer

$$2\pi$$

Question 7

Which trigonometric function is even?

Accepted Answer

Cosine

Question 8

What is the exact value of $$	an \frac{\pi}{4}$$?

Accepted Answer

$$1$$

Question 9

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

Accepted Answer

$$	an 	heta = \frac{1}{\cot 	heta}$$

Question 10

If $$	heta is in $$standard position and its terminal side lies in the second quadrant, what is the reference angle formula?

Accepted Answer

$$	heta' = 180^\circ - 	heta$$

Question 11

Which of the following is the domain of the inverse sine function $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

$$[-1, 1]$$

Question 12

What is the range of the cosine function?

Accepted Answer

$$[-1, 1]$$

Question 13

Which trigonometric function is periodic with period $$\pi$$?

Accepted Answer

Tangent

Question 14

If $$\cos 	heta = -\frac{1}{2}$$ and $$	heta is in$$ $$[0, 2\pi]$$, what are the possible values for $$	heta$$?

Accepted Answer

$$\frac{2\pi}{3}$$ and $$\frac{4\pi}{3}$$

Question 15

Which of the following is the correct definition of a periodic function?

Accepted Answer

A function $$f is $$periodic if $$f(t+p) = f(t)$$ for all $$t in $$the domain of $$f$$ and some positive number $$p.$$

Question 16

What is the exact value of $$\sin \frac{\pi}{6}$$?

Accepted Answer

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

Question 17

Which of the following is the correct domain for the tangent function?

Accepted Answer

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

Question 18

If $$\sin 	heta = -\frac{1}{2}$$ and $$	heta is in$$ $$[0, 2\pi]$$, what are the possible values for $$	heta$$?

Accepted Answer

$$\frac{7\pi}{6}$$ and $$\frac{11\pi}{6}$$

Question 19

Which of the following is the correct formula for converting radians to degrees?

Accepted Answer

Multiply by $$\frac{180^\circ}{\pi}$$

1.4 Trigonometric Functions and Their Inverses

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