If sinx = 1/4 Find the exact value of cos2x

I used the formula for double angle identities :
cos2x = 1-2sin^2x
and got the answer 1/2
The book says the answer is 7/8
How would they get to that conclusion?

Found my mistake ....

All is good now
Thanks for the help earlier Damon
Don

To find the exact value of cos2x when sinx is given, we can use the formula for double angle identities as you did. However, it seems like there may have been an error in your calculations or substitution.

Let's start from the beginning. Given sinx = 1/4, we can find the value of cosx using the Pythagorean identity:

cosx = √(1 - sin^2x) = √(1 - (1/4)^2) = √(1 - 1/16) = √(15/16) = √15/4

Now, substituting cosx into the double-angle identity formula:

cos2x = 1 - 2sin^2x = 1 - 2(1/4)^2 = 1 - 2(1/16) = 1 - 2/16 = 1 - 1/8 = 7/8

Therefore, the correct answer is indeed 7/8.

To find the exact value of cos(2x) given that sin(x) = 1/4, we can use the double angle identity formula for cosine, which states that cos(2x) = 1 - 2sin^2(x).

Step 1: Find sin^2(x)
Since sin(x) = 1/4, we can square both sides:
sin^2(x) = (1/4)^2 = 1/16

Step 2: Substitute sin^2(x) into the double angle identity formula
Using the double angle identity formula for cosine, we substitute sin^2(x) with 1/16:
cos(2x) = 1 - 2(1/16) = 1 - 2/16 = 1 - 1/8

Simplifying further, we can find a common denominator:
cos(2x) = (8/8) - (1/8) = 7/8

Therefore, the exact value of cos(2x) given sin(x) = 1/4 is 7/8.