Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Section 3.1 Radian Measure Radian measure enables us to treat the trigonometric functions as functions with domains (inputs) of REAL NUMBERS, rather than angles. An angle with its vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle has a measure of 1 radian. If is a central angle of a circle of radius , and intercepts an arc of length s, then the radian measure of is found by, How many radians represents a complete rotation? Converting between degrees and radians Since 1 degree radians , radians 1 radian and degrees To convert from 1) degrees to radians, multiply by 2) radians to degrees, multiply by Example 1: Convert each degree measure to radians. Show as a multiple of a) b) and give its decimal approximation. c) Example 2: Convert each radian measure to degrees. NOTE: If no unit of measurement is specified for an angle, then the angle is understood to be in radians. a) 2.92 NOTE: A shortcut to convert radians to degrees: substitute 180 for . b) c) Important degree measures and their radian equivalences Reference angles are super easy to recognize for the radian measures shown here. Reference angle: Reference angle: Reference angle: 30° 45°= √ 60° √ √ √ √ 1 √ Example 3: Find the exact value of each expression without using a calculator. = _________ b) = ________ Quadrant: Quadrant: Reference Angle: Reference Angle: √ √ 1 √ √ √ 2 √ ( c) ) =________ Quadrant: Reference Angle: d) e) = ________ ( ) =________ Quadrant: Reference Angle: