1. 13.2A General Angles
Alg. II

2. Angles In Standard Position
Recall: Angle- formed by two rays that have a common endpoint, called the vertex.
Generated by…
Fixing one ray (the initial side)
Rotating the other ray (the terminal side) about the vertex
Standard position-In a coordinate plane, an angle whose vertex is at the origin and whose initial side is the positive x-axis.

3. Angles in Standard Position
Measure of an angle
Determined by amount and direction of rotation from the initial side to the terminal side.
Positive if the rotation is counterclockwise
Negative if the rotation is clockwise.
(terminal side of an angle can make more than one full rotation)

4. Angles in Standard Position
Terminal side y
90° 0° x
vertex
Initial side
180°
360°
270°

5. Drawing Angles in Standard Position
Example 1- Draw an angle with the given measure in standard position. Then tell in which quadrant the terminal side lies.
a ° b. 400 °
Quadrant I
Quadrant II
Quadrant I
-120 °
400 °
Quadrant IV
Quadrant III

6. Finding Coterminal Angles
Two angles in standard position are coterminal if their terminal sides coincide (or match up).
Can be found by adding or subtracting multiples of 360 ° to the angle.

7. Finding Coterminal Angles
Example 2 – Find one positive and one negative angle that are coterminal with (a) -100 ° and (b) 575 °
Positive coterminal angle: -100 ° ° = 260 °
Negative coterminal angle: -100 ° ° = -460 °
Positive coterminal angle: 575 ° ° = 215 °
Negative coterminal angle: 575 ° ° = -145 °

8. Finding Coterminal Angles
Angles can also be measured in radians.
Radians- the measure of an angle in standard position whose terminal side intercepts an arc length r.
Circumference of circle = 2 π(r), meaning there are 2 π radians in a full circle.
Also meaning (360 ° = 2 π radians) and (180 ° = π radians)

9. 13.2B Conversions Between Degrees and Radians
Degree Measure in Radians
To rewrite, multiply by π radians
180°
Radian Measure in Degrees
To rewrite, multiply by ° .
π radians

10. Converting Between Degrees and Radians
Example 3
Convert 320 ° to radians.
16 π radians 9
b. Convert π radians to degrees. 12
-75 °

11. Arc Lengths & Areas of Sectors
Sector – a region of a circle that is bounded by two radii and an arc of the circle.
Central angle of a sector – the angle formed by two radii.

12. Arc length

13. Ex. 4 Find the arc length and area of sector
With radius of 5 centimeters and a central angle of

14. Ex. 5 Evaluate the trig function using a calc.
(Or tables on pg. 861 & 853) for