Angles in Standard Position and Coterminal Angles

Angles in standard Position

and

Coterminal Angles

Core Vocabulary

• Initial side

• Terminal side

• Standard Position

• Coterminal

• Radian

• Sector

• Central Angle

Drawing Angles in Standard Position

Quadrants

Positive and Negative Angles

The measure of an angle is positive when the rotation of its terminal side is counterclockwise and negative when the rotation is clockwise. The terminal side of an angle can rotate more than 360°.

Drawing a Positive Angle

​Draw 240°

Drawing a Negative Angle

​Draw -50°

Drawing an Angle Greater than 360°

​Draw 500°

Draw

Draw 65° in standard position.

Draw

Draw 300° in standard position.

Draw

Draw -120° in standard position.

Draw

Draw -450° in standard position.

Coterminal Angles

On slide 6, angles 500° and 140° are coterminal because their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of 360°.

Ex: Find one Positive and one Negative Angle that are coterminal with -45° and 395°

​There are many such angles, depending on what multiple of 360° is added or subtracted.

Find one positive and one negative angle that are coterminal with 100°

Find one positive and one negative angle that are coterminal with -205°

Open Ended

Find one positive angle and one negative angle that are coterminal with 80°

Open Ended

Find one positive angle and one negative angle that are coterminal with -135°