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Csc Θ - Cot Θ = Sin Θ, Solve - 2012-05-05

by Zachary
(CA, USA)











































An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

Comments for Csc Θ - Cot Θ = Sin Θ, Solve - 2012-05-05

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May 05, 2012
Csc Θ - Cot Θ = Sin Θ
by: Staff


Question:

by Zachary
(Campbell CA, USA)


An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)




Answer:

Csc Θ - Cot Θ = Sin Θ

Cot(Θ) = Cos(Θ)/Sin(Θ)

Csc Θ = 1/Sin(Θ)

1/Sin(Θ) - Cos(Θ)/Sin(Θ) = Sin Θ

1 - Cos(Θ) = Sin²(Θ)

1 - Sin²(Θ) - Cos(Θ) = 0

cos(2 Θ) = 1 - 2sin²( Θ)

cos(2 Θ) - Cos(Θ) = 0

therefore

2 Θ = Θ

2 Θ - Θ = 0

Θ = 0


>>> the final (approximate) answer is:

Θ ≈ 0° , or 2πk radians

The answer is approximate because the csc and cot cannot be computed for 0°





Thanks for writing.

Staff
www.solving-math-problems.com



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