Question

find the value of theta if 2sin^2theta
=1 by 2

Answer 1

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Answer 2

Value of θ if 2sin²θ  = 1/2 is nπ ± π/6 , Principal Values are  ± π/6 ( ± 30°)

Given:

• 2sin²θ = 1/2

To Find:

• Value of θ

Solution:

Step 1:

Divide both sides by 2

sin²θ = (1/2)(1/2)

sin²θ = (1/2)²

Step 2:

Use sin (π/6) = 1/2  and

Use Identity if sin²θ = sin²α then θ  = nπ ± α

Hence

θ = nπ ± π/6

Value of θ if 2sin²θ  = 1/2 is nπ ± π/6

Principal Values are  ± π/6 or  ( ± 30°)

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