Precalculus Unit 7 Quiz #3: REVIEW name: _______________ 7F – 7H [1.] The current I, in amperes, flowing through an arc (alternating current) circuit at time t, in seconds is: π I(t) = 120 sin (30πt - ), t ≥ 0 3 Find the: period, amplitude, and phase shift. [2.] The following data represent the average monthly temperatures for Juneau, Alaska. month, x Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. temp, °F 24.2 28.4 32.7 39.7 47.0 53.0 56.0 55.0 49.4 42.2 32.0 27.1 [a.] Draw a scatter plot of the data for one period. [b.] Find a sinusoidal function of the form: y = A sin (kx – c) + h that models the data. [c.] Draw the sinusoidal function found in part [b.] [d.] Use a graphing utility to find the sinusoidal function of best fit. [3.] According to the Old Farmer’s Almanac, in Miami, Florida, the number of hours of sunlight on the summer solstice of 2007 was 13.75, and the number of hours of sunlight on the winter solstice was 10.55. Find a sinusoidal function of the form: y = A sin (kx – c) + h that models the data. [4.] A bobber floats on the water, bobbing up and down. The distance between its highest and lowest points is 4 centimeters. It moves from its highest point down to its lowest point and back again in 15 seconds. Write a cosine function that models the movement of the leaf in relationship to the equilibrium point.  ©0 l240o1F4b AKyudtua4 kSHo8fjtJwTacr8eX EL3LaCg.i k tAdlMlB tr1iPgHh3tYsN prIewsEe3r4v5eDdE.C Find the exact value of each trigonometric function. 5) cot    6) csc   7) sin    8) tan   9) sec    10) csc  11) cot   12) sec  13) sin   14) cos 15) tan        16) cos    Graph each function using radians.   17) y sec     ( ) ©1 T2N0u1Y4Q jKmu2twaN LSro5fQtwwra4rqeS NLyLmCF.I K PANltlR crqiqgahtt4sQ CrLepsVeBrXvveldQ.e P BMOahdbeu 0w0iqtFh3 LIHnUf5iBn2iEtre8 kAElagaeib9rxaM r2J.F 18) ycsc -1- (        ) Worksheet by Kuta Software LLC  ( 19) ycot      ) 20) ysec (        ) (      22) y tan     (    24) ycot 21) ytan   23) ycsc   ) ) ©2 P2G0O1M4x tKOuMteaY xSRovfAtBwuaCrfey YLoLLC8.h e qANlalB irVipgthVtnsi KrgebsDeerqvmerds.l f IM4a4dyeK HwJidtlhE GIHnPfaiZnYiKtbe5 tAblNg5erbQrpa7 p2m.J ( -2- (     )    ) Worksheet by Kuta Software LLC Find the exact value of each expression. [25.] cos-1 (-1) [28.] sin-1 (- [26.] arcsin √3 ) 2 3π 8 √3 ) 2 [37.] sec (arcsin (-1)) [40.] sec-1 2√3 3 [27.] tan-1 [29.] arccos (cos [31.] arctan (tan (- [34.] tan (cos-1 (- √2 2 )) 4π 5 9π [32.] sin-1 (sin ( )) 8 1 ) √3 3 π [30.] arcsin (sin (- )) 10 [33.] cos (arcsin [35.] tan (sin-1 (- )) [36.] csc (tan-1 1) [38.] cot (arccos 0) [39.] csc-1 √2 2 [41.] cot-1 (- √3 ) 3 [42.] csc-1 (-1) √2 ) 2