Q: Which of the following is true for the range of the secant function?

$$\sec \theta \leq -1 or$$ $$\sec \theta \geq 1$$

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

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

Q: Which of the following is true for the range of the tangent function?

$$-\infty \u003c \tan \theta \u003c \infty$$

Q: Which of the following is the correct even-odd property for the secant function?

$$\sec(-\theta) = \sec \theta$$

Question 1

Let $$P = \left(-\frac{3}{2}, -\frac{1}{2}\right) be a $$point on the unit circle corresponding to a real number $$t. $$What is $$\sec t$$?

Accepted Answer

$$-2\sqrt{3}$$

Question 2

Given the point $$(-3, 4) on $$the terminal side of angle $$	heta$$, what is $$	an 	heta$$?

Accepted Answer

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

Question 3

Which of the following best describes the domain of the tangent function?

Accepted Answer

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

Question 4

What is the range of the sine function?

Accepted Answer

$$-1 \leq \sin 	heta \leq 1$$

Question 5

Which property is illustrated by $$\sin(	heta + 2\pi) = \sin 	heta$$?

Accepted Answer

Periodic property

Question 6

If $$\cos(-	heta) = \cos 	heta$$, what type of function is cosine?

Accepted Answer

Even function

Question 7

Find the exact value of $$\sin(765^\circ).$$

Accepted Answer

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

Question 8

Which of the following is true for the range of the secant function?

Accepted Answer

$$\sec 	heta \leq -1 or$$ $$\sec 	heta \geq 1$$

Question 9

If $$f(	heta) is $$periodic with period $$p$$, which equation must be satisfied?

Accepted Answer

$$f(	heta + p) = f(	heta)$$

Question 10

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

Accepted Answer

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

Question 11

Given $$\sin(-30^\circ)$$, what is its value?

Accepted Answer

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

Question 12

Which of the following is NOT in the domain of the cotangent function?

Accepted Answer

$$	heta = \pi$$

Question 13

If $$	an(	heta + \pi) = 	an 	heta$$, what does this say about the period of the tangent function?

Accepted Answer

The period is $$\pi$$

Question 14

If $$\sin 	heta = \frac{4}{5}$$ and $$	heta is in $$the second quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{3}{5}$$

Question 15

Which of the following is an odd function?

Accepted Answer

$$	an 	heta$$

Question 16

If $$\sin 	heta = b$$ and $$\cos 	heta = a$$ for a point $$P = (a, b) on $$the unit circle, what is $$	an 	heta$$?

Accepted Answer

$$\frac{b}{a}$$

Question 17

Which of the following is true for the range of the tangent function?

Accepted Answer

$$-\infty \u003c 	an 	heta \u003c \infty$$

Question 18

If $$\cos(3\pi) = x$$, what is $$x$$?

Accepted Answer

$$-1$$

Question 19

Which of the following is the correct even-odd property for the secant function?

Accepted Answer

$$\sec(-	heta) = \sec 	heta$$

Question 20

A Ferris wheel rotates such that the height $$h (in $$meters) above the ground of a seat at time $$t (in $$seconds) is modeled by $$h(t) = 10 + 8\sin\left(\frac{\pi}{15} t\right). $$What is the maximum height reached by the seat?

Accepted Answer

$$18$$ meters

Unit Circle Approach and Properties of Trigonometric Functions

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