Use a double-angle formula to find the exact value of cos2x when sinx = 3/5, where pi/2 < x < pi.

-(7/25) or 7/25?

well, just keep track of the signs as you work it out.

cos2x = 1 - 2sin^2x = 1 - 2*9/25 = 7/25

Or, if you insist on doing it the hard way,

cos2x = cos^2x - sin^2x = 16/25 - 9/25 = 7/25

If you came up with -7/25, you need to remember your simple Algebra I!

To find the exact value of cos2x using a double-angle formula, we first need to determine the value of cosx.

Given that sinx = 3/5 and pi/2 < x < pi, we know that x lies in the second quadrant. In the second quadrant, sinx is positive, and cosx is negative.

Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can find cosx:
(3/5)^2 + cos^2(x) = 1
9/25 + cos^2(x) = 1
cos^2(x) = 1 - 9/25
cos^2(x) = 16/25

Since cosx is negative in the second quadrant, we take the negative square root:
cosx = -4/5

Now, we can use the double-angle formula for cosine to find cos2x:
cos2x = 2cos^2(x) - 1
cos2x = 2(-4/5)^2 - 1
cos2x = 2(16/25) - 1
cos2x = 32/25 - 1
cos2x = 32/25 - 25/25
cos2x = 7/25

Therefore, the exact value of cos2x when sinx = 3/5 is 7/25.