13.2 angles and angle measure objectives: 1.change radian measure to degree measure and vice-versa....

13.2 Angles and Angle Measure

Objectives:1. Change radian measure to degree

measure and vice-versa.2. 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-axisTerminal side – the other ray that can rotate about the centerStandard 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 AnglesDraw an angle with the

given measure in standard position.

1. 210°2. 540°

540-360=1803. -45°

1.

2.

3.

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°

180

5

4

5 180

4

225

180

75180

5

12

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.

1. 210°210+360=570°210-360=-150°

2. 73

7 7 6 132

3 3 3 3

7 6

3 3 36 5

3 3 3

Homeworkp. 712

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