Converting between Radians and Degrees

Converting between Radians and Degrees

By Mrs. Chestleigh

An angle on the coordinate plane is in standard form when vertex is on the origin and one ray lies on the x-axis.

• The ray on the x-axis is called the initial side

• The other ray is called the terminal side.

angles in standard form

Angles in standard form

Counterclockwise rotations result in positive angle measures.

• Clockwise rotations result in negative angle measures.

• One full revolution = 360 degrees

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Remember that the initial side is on the x-axis, and the terminal side is the angle formed with the initial side.

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Example. sketch the angle, -75 degrees, in standard form

Draw

Sketch the angle, -30 degrees, in standard form. Use different colors for the initial side and the terminal side.

Remeber the initial side starts at the x-axis, and the terminal side forms the angle with the initial side.

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Example 2. Sketch the angle, 160 degrees, in standard form.

Draw

Sketch the angle, 145 degrees, in standard form.

Remember, a full revolution is 360 degrees. The reference angle, drawn in blue, is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the x-axis.

To find the reference angle, simply subtract 360 from 400.​

400 - 360 = 40​

​example 3. sketch the angle, 400 degree, in standard form.

Multiple Choice

Which of the following is the reference angle to 540 degrees?

• -280

• -180

• 280

• 180