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alex41 [277]
2 years ago
14

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places

where appropriate.) sin theta = 1/2 Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) cos theta = -1
Mathematics
1 answer:
Montano1993 [528]2 years ago
3 0

The solution of the given equation is :

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

Since cos2θ + sin2θ = 1, sin2θ = 1 - cos2θ

So, the given equation is equivalent to 2(1 - cos2θ) - cosθ = 1

-2cos2θ - cosθ + 1 = 0

2cos2θ + cosθ - 1 = 0 (multiplying the entire equation by -1)

(2cosθ - 1)(cosθ + 1) = 0 (taking common)

cosθ = 1/2 or cosθ = -1 (on equating it to zero)

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

For more information about trigonometric ratios, visit

brainly.com/question/24496175

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