# Cos 2Θ = 5Sin Θ - 2, Solve equation - 2012-05-05

by Zachary
(CA, USA)

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

### Comments for Cos 2Θ = 5Sin Θ - 2, Solve equation - 2012-05-05

 May 05, 2012 Cos 2Θ = 5Sin Θ - 2 by: Staff Question: by Zachary (Campbell CA, USA) Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) Answer: Cos 2Θ = 5Sin Θ - 2 cos(2 Θ) = 1 - 2sin²( Θ) 1 - 2sin²( Θ) = 5Sin Θ - 2 -1 + 2sin²( Θ) = -5Sin Θ + 2 2sin²( Θ) + 5Sin Θ - 3= 0 Substitute x for sin(Θ) 2x² + 5x - 3 = 0 x² + 5x/2 - 3/2 = 0 (x – ½)(x + 3) = 0 x ∈ {-3, ½} Substitute sin(Θ) for x If x = -3 sin(Θ) = -3 Θ = sin⁻¹(-3) Θ = cannot be determined If x = 1/2 sin(Θ) = 1/2 Θ = sin⁻¹(1/2) Θ = 30°, or π/6 radians Or Θ = 150°, or 5π/6 radians >>> the final answer is: Θ = 30°, or π/6 radians Or Θ = 150°, or 5π/6 radians Thanks for writing. Staff www.solving-math-problems.com