39 O1 points SAgTrig4 75009 Solve the given equation Enter y

39. O-1 points SAgTrig4 7.5.009 Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places cos(28)-9 sin(9-4 Need Help? eadWwich Watch 40 -1 points SAigTrig4 7.5.020.MI An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places whe 2 sin(30) + 1-0 (a) Find all solutions of the equation. (b) Find the solutions in the interval [o, 2m). Need Heip? liReaon Mac.

Solution

co2theta = 9sintheta -4

1-2sin2^2theta = 9sintheta -4

2sin^2(theta) + 9sintheta -5 =0

Solve the quadratic:

2sin^2theta +10sintheta -sintheta -5=0

2sintheta(sintheta+5) -1(sintheta +5) =0

((2sintheta -1) )( 5+ sintheta) =0

sintheta = -5 (Neglect as sin cannot be less than -1)

sintheta = 1/2

theta = pi/6 +2k*pi

theta = 5pi/6 +2k*pi