Anonymous

# 21. If sin θ = 1/4 and 0 ≤ θ ≤ π/2 ?

(a) determine the EXACT value of cos 2θ

(b) determine the EXACT value of sin( θ/2)

### 3 Answers

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- ?Lv 76 months ago
a) cos2θ = 1 - 2sin²θ

so, 1 - 2(1/4)² => 7/8

b) cosθ = 1 - 2sin²(θ/2)

Now, cosθ = ±√15/4

As 0 ≤ θ ≤ π/2, cosθ = √15/4

so, √15/4 = 1 - 2sin²(θ/2)

i.e. 2sin²(θ/2) = (4 - √15)/4

=> sin²(θ/2) = (4 - √15)/8

Hence, sin(θ/2) = √[(4 - √15)/8]

:)>

- alexLv 76 months ago
0 ≤ θ ≤ π/2 ---> cosθ >0 , sin( θ/2) >0

identity

(sinθ)^2 + ( cosθ)^2=1

and

formula

cos(2θ) = (cosθ)^2 - (sinθ)^2 = 1- 2(sin(θ))^2

you can do

- Anonymous6 months ago
Refer to the answers for the many similar questions you have recently posted.

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