Q: Which of the following is a Pythagorean identity?

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

Q: Decide whether $$\sec\theta = 0.6 is $$possible for any angle $$\theta.$$

Impossible, because $$\sec\theta \leq -1 or$$ $$\sec\theta \geq 1$$

Q: For the point $$(100, -6) on $$the terminal side of $$\theta$$, what is $$\sin\theta$$?

$$\sin\theta = \frac{-6}{\sqrt{100^2$ + (-6)^2$}}$$

Q: Which of the following is a reciprocal identity?

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

Q: If $$\theta is in $$quadrant IV and $$\sin\theta = -\frac{1}{2}$$, what is $$\sec\theta$$?

$$\sec\theta = \frac{1}{\sqrt{1 - \sin^2$\theta}}$$

Q: Which of the following is the correct quotient identity?

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

Q: If $$\sin\theta = 0.8$$ and $$\theta is in $$quadrant II, what is $$\cos\theta$$?

$$\cos\theta = -\sqrt{1 - 0.8^2$}$$

Question 1

Given a point $$P(x, y) on $$the terminal side of an angle $$	heta in $$standard position, what is the formula for $$r$$, the distance from the origin to $$P$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$

Question 2

If the terminal side of an angle $$	heta$$ passes through $$(-3, -4)$$, what is $$\sin	heta$$?

Accepted Answer

$$\sin	heta = \frac{-4}{5}$$

Question 3

Which trigonometric functions are undefined for an angle whose terminal side lies along the y-axis?

Accepted Answer

Tangent and secant

Question 4

Given $$\sec	heta = \frac{5}{3}$$, what is $$\cos	heta$$?

Accepted Answer

$$\cos	heta = \frac{3}{5}$$

Question 5

If $$	an	heta = \frac{4}{3}$$ and $$	heta is in $$quadrant III, what is $$\sin	heta$$?

Accepted Answer

$$\sin	heta = -\frac{4}{5}$$

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

If $$	heta is in $$quadrant II, which trigonometric functions are positive?

Accepted Answer

Sine and cosecant

Question 8

Decide whether $$\sec	heta = 0.6 is $$possible for any angle $$	heta.$$

Accepted Answer

Impossible, because $$\sec	heta \leq -1 or$$ $$\sec	heta \geq 1$$

Question 9

If $$\sin	heta \u003e 0$$ and $$	an	heta \u003c 0$$, in which quadrant is $$	heta$$?

Accepted Answer

Quadrant II

Question 10

A downhill highway grade is modeled by $$y = -0.06x. $$What is the grade of the road?

Accepted Answer

-6%

Question 11

For the point $$(100, -6) on $$the terminal side of $$	heta$$, what is $$\sin	heta$$?

Accepted Answer

$$\sin	heta = \frac{-6}{\sqrt{100^2$ + (-6)^2$}}$$

Question 12

Which of the following is a reciprocal identity?

Accepted Answer

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

Question 13

If $$\cos	heta \u003c 0$$ and $$\sec	heta \u003c 0$$, in which quadrant(s) could $$	heta be$$?

Accepted Answer

Quadrant II or III

Question 14

Which trigonometric function can take any real value?

Accepted Answer

Tangent

Question 15

If the terminal side of an angle passes through $$(-3, 0)$$, which trigonometric functions are undefined?

Accepted Answer

Cotangent and cosecant

Question 16

If $$	heta is in $$quadrant IV and $$\sin	heta = -\frac{1}{2}$$, what is $$\sec	heta$$?

Accepted Answer

$$\sec	heta = \frac{1}{\sqrt{1 - \sin^2$	heta}}$$

Question 17

Which of the following is the correct quotient identity?

Accepted Answer

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

Question 18

If $$\sin	heta = 0.8$$ and $$	heta is in $$quadrant II, what is $$\cos	heta$$?

Accepted Answer

$$\cos	heta = -\sqrt{1 - 0.8^2$}$$

Question 19

A 3000-pound car is on a highway with grade $$-6\%. $$What is the approximate grade resistance force acting on the car?

Accepted Answer

180 pounds

The Unit Circle and the Functions of Trigonometry: Definitions, Properties, and Applications

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