1. Measuring Angles

If an angle $c$ in standard position has its terminal side passing through the point $(0,1)$, what is the measure of $c$ in degrees?

Which of the following angles in standard position corresponds to a point on the negative $y$-axis?

If $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$ are two angles in standard position, which angle has a measure equal to the sum of $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$?

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I: 1.

cot⁻¹ 30

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858

F. 1.962610506

G. 14.47751219°

H. 1.015426612

I. 1.051462224

J. 0.9925461516

In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.

tan θ > 0 and sec θ > 0

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (0, -2)

Given a right triangle where angle $ACB$ is one of the non-right angles and the side opposite angle $ACB$ is $4$ units while the side adjacent to angle $ACB$ is $3$ units, which is the approximate measure of angle $ACB$?

If angle $BAC$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $BAC$ in degrees?

If an angle $\mathrm{lkj}$ in standard position has a terminal side that passes through the point $(7,6)$ on the coordinate plane, what is the measure of angle $\mathrm{lkj}$ in degrees, rounded to the nearest whole degree?

In standard position, if $\theta$ = $53°$, what is the reference angle?

Find the angle of least positive measure that is coterminal with each angle. 792°

Given that angle $psq$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $psq$ in degrees?

Given that angle $tsu$ is in standard position and its terminal side passes through the point $(0,1)$ on the unit circle, what is the measure of angle $tsu$ in degrees?

An angle measuring $154°$ in standard position is classified as which type of angle?

If ray $\overrightarrow{\mathrm{AB}}$ is rotated counterclockwise about the origin to coincide with ray $\overrightarrow{\mathrm{AC}}$ in standard position, and the measure of angle $\angle BAC$ is $120$ degrees, how many degrees has $\mathrm{ABC}$ been rotated counterclockwise about the origin?