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33 votes
33 votes
Solve on the interval [0, 2pi):1 + sin theta = 1/2

User Jay Carlton
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1 Answer

24 votes
24 votes

You have the following equation:

1 + sinθ = 1/2

in order to solve the previous equation for θ, proceed as follow:

1 + sinθ = 1/2 subtract 1 both sides

sinθ = 1/2 - 1 simplify right sides

sinθ = -1/2 apply sin⁻¹ both sides to cancel sin left side

sin⁻¹(sinθ) = sin⁻¹(-1/2)

θ = sin⁻¹(-1/2)

θ = -30°

-30° is the same as 360° - 30° = 330°

Hence, the value of θ is 330°

User Florian Hansen
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2.9k points