1. Measuring Angles

If angles $PTQ$ and $STR$ are vertical angles and congruent, which of the following statements is true about their measures in standard position?

In standard position, if ray $OX$ is the initial side and ray $OZ$ is the terminal side, what is the name of the angle formed by these two rays?

Given that angle $\mathrm{BAC}$ is in standard position and its terminal side passes through the point $(3,4)$ on the coordinate plane, what is the degree measure of angle $\mathrm{BAC}$? Round to the nearest whole degree.

Which of the following angles in standard position is considered to represent a low projection ($\mathrm{elevation}$)?

Given an angle of $60°$ in standard position, which of the following angles is coterminal with it?

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

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. tan θ = 4.6252

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

Column I: 1. sin 83°

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

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. 112° 15'

Find the measure of the smaller angle formed by the hands of a clock at the following times. 3:15

Perform each calculation.

110° 25' + 32° 55'

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.

cot 𝜋/12

Which angle is adjacent to $\frac{\pi }{4}$ on the unit circle?

If an angle in standard position has its terminal side passing through the point $(1,2)$, which of the following is closest to the measure of the angle in degrees?

Which of the following angles is a right angle in standard position?