12 2 Angles and Angle Measure Standard Position

�Standard Position – when the vertex of the angle is at the origin and

Example 1: Draw an angle with the given measure in standard position. a. 210°

Example 2: a. In a springboard diving competition, a diver made a 900 -degree

Example 2: b. While riding down the mountain, a snowboarder goes off a jump

Coterminal Angles: - Two or more angles in standard position with the same terminal

Example 3: Find an angle with a positive measure and an angle with a

Example 4: Conversions a. Rewrite 30° in radians. b. Rewrite 120° in radians.

- Central Angle – an angle with a vertex at the center of the

Example 6: a. The steering wheel on a monster truck has a radius of

Example 6: b. The steering wheel on a yacht has a radius of 16

Slides: 16

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12. 2 – Angles and Angle Measure

�Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. �Initial Side – the ray on the x-axis. (where the angle starts. ) �Terminal Side - the ray that rotates about the center. (where the angle ends. )

Example 1: Draw an angle with the given measure in standard position. a. 210° b. – 45°

Example 2: a. In a springboard diving competition, a diver made a 900 -degree rotation before slicing into the water. Draw an angle in standard position that measures 900°.

Example 2: b. While riding down the mountain, a snowboarder goes off a jump and turns 600° before touching down onto the snow again. Determine how many degrees past the positive x-axis the snowboarder lands.

Coterminal Angles: - Two or more angles in standard position with the same terminal side. - How can we find coterminal angles? ? ?

Example 3: Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle. a. 210° b. – 120°

Radians: �

Example 4: Conversions a. Rewrite 30° in radians. b. Rewrite 120° in radians.

Example 5: Conversions �

- Central Angle – an angle with a vertex at the center of the circle.

Example 6: a. 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?

Example 6: b. The steering wheel on a yacht has a radius of 16 inches. How far does a point on the steering wheel travel if the wheel makes five sevenths of a rotation?