Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

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

Relevance
  • ?
    Lv 7
    6 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] 

    :)>

  • alex
    Lv 7
    6 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

  • Anonymous
    6 months ago

    Refer to the answers for the many similar questions you have recently posted.

Still have questions? Get your answers by asking now.