13.2A General Angles Alg. II

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.

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)

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

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. -120 ° b. 400 ° Quadrant I Quadrant II Quadrant I -120 ° 400 ° Quadrant IV Quadrant III

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.

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 ° + 360 ° = 260 ° Negative coterminal angle: -100 ° - 360 ° = -460 ° Positive coterminal angle: 575 ° - 360 ° = 215 ° Negative coterminal angle: 575 ° - 720 ° = -145 °

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)

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 180° . π radians

Converting Between Degrees and Radians Example 3 Convert 320 ° to radians. 16 π radians 9 b. Convert - 5 π radians to degrees. 12 -75 °

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.

Arc length

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

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