compute the following in terms of x

Question

Assume sin⁡(θ)=x/11 where 0<θ<π/2. Compute the following in terms of x.

cos⁡(2θ)= 

tan⁡(θ/2)= 

Answer 1

If sin(θ) = x/11, then cos(θ) = sqrt(1-x²/121)

cos(2θ) = cos²(θ)-sin²(θ) = (1-x²/121) - x²/121

tan(θ/2) = +/- (1 - cos(θ))/sin(θ) (This form is easier to deal with than sqrt((1-cos(θ))/(1+cos(θ))

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