Solve the following equation for : 0<x<pie: 2cos^x+3sinx-3=0 Select all that apply.

0

pie/6

pie/2

5pie/6

cos^2(x) = 1 - sin^2(x) (Pythagorean identity) 2(1 - sin^2(x)) + 3sin(x) - 3 = 0 (substitution) 2 - 2sin^2(x) + 3sin(x) - 3 = 0 (distributive prop) -2sin^2(x) + 3sin(x) - 1 = 0 (combining like terms) 2sin^2(x) - 3sin(x) + 1 = 0 (X both sides by -1) (2sin(x) - 1)(sin(x) - 1) = 0 (factored LHS) 2sin(x) - 1 = 0 or sin(x) - 1 = 0 (zero product rule) sin(x) = 1/2 or sin(x) = 1 (solve for sin(x)) x = 30 deg, 150 deg or 90 deg (sin(30 deg) = sin(150 deg) = 1/2, sin(90 deg) = 1 In radians, your answers are pi/6, 5pi/6, pi/2.

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