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2 sin^2 theta + 3 cos theta = 3​

1 Answer

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Answer:

θ = ±π/3 + 2kπ

θ = 0 + 2kπ

Explanation:

2 sin² θ + 3 cos θ = 3

Use Pythagorean identity:

2 (1 − cos² θ) + 3 cos θ = 3

2 − 2 cos² θ + 3 cos θ = 3

0 = 2 cos² θ − 3 cos θ + 1

Factor:

0 = (2 cos θ − 1) (cos θ − 1)

cos θ = 1/2

θ = ±π/3 + 2kπ

cos θ = 1

θ = 0 + 2kπ

User Zhenhir
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