Draw an Angle in Standard Position

A. Draw an angle with a measure of 210° in standard position.

210° = 180° + 30°

Draw the terminal side of the angle 30° counterclockwise past the negative x-axis.

Answer:

Draw an Angle in Standard Position

B. Draw an angle with a measure of –45° in standard position.

Answer:

The angle is negative. Draw the terminal side 45° clockwise from the positive x-axis.

Find Coterminal Angles

A. Find an angle with a positive measure and an angle with a negative measure that are coterminal with 210°.

positive angle: 210° + 360° = 570°

negative angle: 210° – 360° = –150°

Answer: 570° and –150°

Find Coterminal Angles

B. Find an angle with a positive measure and an angle with a negative measure that are coterminal with –120°.

positive angle: 120° + 360° = 240°

negative angle: 120° – 360° = –480°

Answer: 240° and –480°

Convert Between Degrees and Radians

A. Rewrite 30° in radians.

Answer:

Convert Between Degrees and Radians

Answer: –300°

B. Rewrite in degrees.

Find Arc Length

TRUCKS The steering wheel on a monster truck has a radius of 11 inches. How far does a point on the steering wheel travel if the wheel makes four fifths of a rotation?

Step 1 Find the central angle in radians.

Find Arc Length

≈ 55.3 in. Use a calculator to simplify.

Answer: A point on the steering wheel will travel about 55.3 inches after four fifths of a rotation.

Step 2 Use the radius and the central angle to find the arc length.

s = r Write the formula for arc length.