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

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.

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.