1. Measuring Angles

Given an angle $yzx$ in standard position, which of the following is the closest to its measure in degrees?

If an angle $\angle ABD$ is in standard position and its terminal side passes through the point $(3,4)$, what is the measure of $\angle ABD$ to the nearest degree?

Given two angles in standard position, $m_1$ = $27°$ and $m_2$ = $25°$, what is the measure of the angle formed by rotating from the initial side of $m_2$ to the terminal side of $m_1$ in the positive (counterclockwise) direction?

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 102.3771°

Given the points $17°$, $75°$, $149°$, and $211°$ on a circle, what is the measure in degrees of the minor arc from $75°$ to $149°$?

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. tan θ = 0.4169

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

tan θ = 6.4358841

Perform each calculation. See Example 3. 47° 29' ― 71° 18'

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

cos 𝜋/10

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

cos(90°-3.69°)

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

cos 41° 24'

Given that $\angle PQR$ is an angle in standard position with its initial side along the positive x-axis and its terminal side passing through the point $(3,4)$, what is the measure of $\angle PQR$ in degrees?

In a regular pentagon, what is the measure in degrees of each interior angle?

If an angle $\theta$ is in standard position and its terminal side passes through the point $(1,1)$ on the coordinate plane, what is the measure of $\theta$ in degrees?

Given that angle $wxy$ is in standard position and its terminal side passes through the point $(3,9)$, what is the measure of angle $wxy$ to the nearest degree?