Question 1

Given a right triangle with legs of lengths 7 and 24, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{7^2$ + 24^2$}$$

Question 2

If the points $$P(2, 3)$$ and $$R(6, 7)$$ are given, what is the distance between them using the distance formula?

Accepted Answer

$$\sqrt{(6-2)^2$ + (7-3)^2$}$$

Question 3

Which of the following is the correct definition for $$\sin 	heta in $$terms of $$x$$, $$y$$, and $$r$$?

Accepted Answer

$$\sin 	heta = \dfrac{y}{r}$$

Question 4

If the point $$(12, 5) is on $$the terminal side of angle $$	heta in $$standard position, what is $$r$$?

Accepted Answer

$$\sqrt{12^2$ + 5^2$}$$

Question 5

Given the point $$(8, -6) on $$the terminal side of $$	heta$$, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{8}{\sqrt{8^2$ + (-6)^2$}}$$

Question 6

If $$	heta is a $$quadrantal angle with its terminal side on the positive $$y-$$axis, what is $$\sin 	heta$$?

Accepted Answer

$$1$$

Question 7

Which trigonometric function is undefined for $$	heta = 90^\circ$$?

Accepted Answer

$$	an 	heta$$

Question 8

If $$	heta is in $$Quadrant II and $$\dfrac{y}{r} is $$considered, is the ratio positive or negative?

Accepted Answer

Positive

Question 9

Suppose $$	heta is in $$Quadrant III. Is $$\dfrac{y}{x}$$ positive or negative?

Accepted Answer

Positive

Question 10

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

Accepted Answer

$$-1$$

Question 11

Which of the following is the correct formula for the distance between points $$P(x_1$, y_1$)$$ and $$R(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$-x_1$)^2$$ + ($$y_2$$-$$y_1)^2$}$$

Question 12

Which trigonometric function is always positive in Quadrant I?

Accepted Answer

All six trigonometric functions

Question 13

If $$	heta = 360^\circ$$, what is $$\cos 	heta$$?

Accepted Answer

$$1$$

Question 14

Which of the following is the correct definition for $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \dfrac{r}{x}$$

Question 15

If $$	an(-900^\circ) is $$evaluated, what is the result?

Accepted Answer

$$0$$

Question 16

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the base of the ladder is 3 meters from the wall and the ladder is 5 meters long, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{3}{5}$$

Question 17

If $$	heta is a $$quadrantal angle and its terminal side lies on the negative $$x-$$axis, what is $$	an 	heta$$?

Accepted Answer

$$0$$

Question 18

Which of the following is the correct definition for $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \dfrac{x}{y}$$

Question 19

If the equation $$3x - 2y = 0$$ defines the terminal side of $$	heta$$ and $$x \leq 0$$, which quadrant does $$	heta$$ lie in?

Accepted Answer

Quadrant II

Trigonometric Functions: Definitions, Properties, and Applications

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