Precalculus and Modeling Podners _ Pod Work - Solving Trig Equations and Inequalities 1. [6 pts] Find all solutions to the equation sin(0) = 3 cos?(0) - 1. All approximate solutions should be rounded to the nearest thousandth. Show your work clearly. sin(8)= 3cos"(4) -1 sink = 2 x = sin( ? ) 3 cos ( 0) ? - sin ( 0 ) - 1 x = 0. 62 3 (1 - sin ?(0) ) - since ) - 1 - 3 sin ? (0 ) - sin (8 ) + 2 Sinx = -1 X = 3n 2 3 x + x + 2 : 0 (3 x - 2) ( x + 1 ) = 0 *= - 2.542 + ann 3 x- 2 = 0 +2 + 2 x +1 =0 -1 3x = 2 X = -1 x = 31 + 2nn 3 3 a x = 3 2. [6 pts] Find all solutions to the equation cos (20) + 3 = 5cos (0) in the interval [-2nt, 27]. Write your answers in exact form (known angles) if possible. cos ( 20) + 3 = 5cos(8) cos ( 20) - 5cos (6) + 3=0 2 cos x - Ocos* + 3 = 0 COS X-= 1 COSX = 33. The temperature on a normal spring day in Durham is a sinusoidal function of time. The temperature begins at 559F at 6am and reaches a maximum at noon of 72F. The temperature falls back to 55F by 6pm and drops to 38 F by midnight. This cycle continues for a number of days. a) [1 pt] Sketch a graph of the temperature in Durham over 48 hours. 72 12 38 16 12:18 24 30 36 4248 b) [3 pts] Write a function F(t) that describes the temperature in Durham (in degrees Fahrenheit) at time t, where t represents the number of hours since 6am. 78 17sing ( 72x) + 55 55 amp: 17 midline : 4=55 c) [4 pts] A high school biology class wants to put some potted seeds outside during the times of day when the temperature is warm enough for the seeds to germinate. If the temperature needs to be at least 60F for the seeds to germinate, during what times of the day can the class leave the pots of seeds outside