Use a double angle formula to find the exact value of cos2u when sinu = 3/5, where pi/2 < u < pi.

Question

options

a. cos2u=2/25

b. cos2u=12/25

c. cos2u= 24/25

d. cos2u= 7/25

e. cos2u= -32/25

Please help. Thanks

Answer 1

First find the double angle formula you will use. In this case we will use the formula that contains only the sin(x) function because that is what is given in the problem.

cos(2x) = 1 - 2sin²(x)

our problem uses the letter u instead of x, but that’s ok. The same formula can be used we just replace the x’s with

cos(2u) = 1 - 2sin²(u)

Because sin(u) = 3/5 we will replace sin(u) in the formula with 3/5

cos(2u) = 1 - 2(3/5)²

Now just perform the operations to get your answer:

= 1 - 2(9/25)

= 1 - (18/25)

= (25/25) - (18/25)

= 7/25

The Correct Answer is: 7/25