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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