668 CHAPTER 6 The Circular Functions and Their Graphs Chapter 6Test Prep Key Terms 6.1 radian circumference latitude sector of a circle subtend degree of curvature nautical mile statute mile longitude 6.2 unit circle circular functions reference arc linear speed angular speed unit fraction 6.3 periodic function period sine wave (sinusoid) amplitude 6.4 phase shift argument 6.5 vertical asymptote 6.6 addition of ordinates abscissa ordinate 6.7 simple harmonic motion frequency damped oscillatory motion envelope Quick Review Concepts Examples 0 u = 1 radian y x r r U Convert 135° to radians. 135° = 135 a p 180 radianb = 3p 4 radians Convert - 5p 3 radians to degrees. - 5p 3 radians = - 5p 3 a 180° p b = -300° 6.1 Radian Measure 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. 180° =P radians Degree / Radian Relationship Converting between Degrees and Radians • Multiply a degree measure by p 180 radian and simplify to convert to radians. • Multiply a radian measure by 180° p and simplify to convert to degrees. Arc Length The length s of the arc intercepted on a circle of radius r by a central angle of measure u radians is given by the product of the radius and the radian measure of the angle. s =r U, where U is in radians Area of a Sector The area of a sector of a circle of radius r and central angle u is given by the following formula. = 1 2 r2 U, where U is in radians Find the central angle u in the figure. u = s r = 3 4 radian Find the area of the sector in the figure above. = 1 2 1422 a 3 4b = 6 sq units 0 r = 4 s = 3 u
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