13.2 Angles and Angle Measure

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Presentation transcript:

13.2 Angles and Angle Measure Objectives: Change radian measure to degree measure and vice-versa. Identify coterminal angles.

Angles on a coordinate plane Parts of an angle on a coordinate plane: Initial side – a ray fixed along the positive x-axis Terminal side – the other ray that can rotate about the center Standard Position – when the vertex is at the origin and the initial side is on the positive x-axis

Types of measures Positive Angle 225° Negative Angle -135°

Angles more than 360° For each revolution, add 360°, plus the other angle. The angle is 130°+360°= 490°.

Drawing Angles 1. 2. 3. Draw an angle with the given measure in standard position. 210° 540° 540-360=180 3. -45°

Radians Radian measure is another unit used to measure angles. It is based on the concept of a unit circle which is a circle with a radius of 1 whose center is at the origin. If the radius is 1, the circumference is 2π so 2π is the same as 360°. Smaller angles are fractional parts of 2π.

Unit Circle

Changing from radians to degrees or from degrees to radians Radians to degrees – Multiply the number of radians by Example: Degrees to radians – Multiply the number of degrees by Example: 75°

Coterminal Angles Coterminal Angles are angles in standard position with the same terminal side such as 30° and 390°. To find additional angles with the same coterminal angle, add multiples of 360 or subtract multiples of 360. For radian measure, add multiples of 2π or subtract multiples of 2π.

Example: Find one angle with positive measure and one angle with negative measure coterminal with each angle. 210° 210+360=570° 210-360=-150° 2.

Homework p. 712 20-54 even