12.2 – angles and angle measure. standard position – when the vertex of the angle is at the...

12.2 – Angles and Angle Measure

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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.)

Page 3: 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

Page 4: 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

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

a. 210°b. –45°

Page 5: 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

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°.

Page 6: 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

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.

Page 7: 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

Coterminal Angles:- Two or more angles in standard position

with the same terminal side.

- How can we find coterminal angles???

Page 8: 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

Example 3:Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle.

b. 210°b. –120°

Page 9: 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

Radians:- Units that are based on arc length.- The measure of an angle in standard

position with a terminal side that intercepts an arc with the same length as the radius of the circle.

- radians = 360- So how many degrees is radians?

Page 10: 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

Page 11: 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

Example 4: Conversionsa. Rewrite 30° in radians.

b. Rewrite 120° in radians.

Page 12: 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

Example 5: Conversions

a. Rewrite in degrees.

b. Rewrite in degrees.

Page 13: 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

Page 14: 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

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

Page 15: 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

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?

Page 16: 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

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?

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