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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

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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



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