
Bradford T. answered 12/03/21
Retired Engineer / Upper level math instructor
sin2θ=2sinθcosθ
cosθ = √(1-sin2θ) = √(1-0.34312) = 0.93929 (Positive since QI)
sin2θ = 2(0.3431)(0.93929) = 0.6445
Khalid H.
asked 12/03/21Bradford T. answered 12/03/21
Retired Engineer / Upper level math instructor
sin2θ=2sinθcosθ
cosθ = √(1-sin2θ) = √(1-0.34312) = 0.93929 (Positive since QI)
sin2θ = 2(0.3431)(0.93929) = 0.6445
sinx = 0.3432, x = about 20.06 degrees
2x = about 40.12 degrees
sin2x = 0.644
or another way to do this problem is use the trig identity for double sine
sin2x = 2sinxcosx = 2(.3431(.939) = 0.644
if sinx = .3431 use a calculator with an inverse trig function to find x, and then find cosx
cos20.06 = about .939
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