Find cos(2x) if sin = 7/25 and x lies in quadrant 1

My answer was 336/625 but this was wrong. I do not know how to figure this out.

cos 2x = 1 - 2sin^2 x

= 1 - 2(49/625) = 527/625

To find cos(2x) given sin(x) and the quadrant in which x lies, you can use the Pythagorean identity and the double angle formula.

1. First, find the value of cos(x) using the given sin(x) value and the quadrant information.
Since sin(x) = 7/25 and x lies in quadrant 1, we know that both sin(x) and cos(x) are positive.
To find cos(x), we can use the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
Plugging in the value of sin(x) = 7/25, we have (7/25)^2 + cos^2(x) = 1.
Solving for cos(x), we get cos(x) = √( 1 - (7/25)^2 ) ≈ √( 1 - 49/625 ) = √576/625 = 24/25.

2. Now, use the double angle formula for cosine to find cos(2x):
cos(2x) = 2cos^2(x) - 1.
Plugging in the value of cos(x) found in step 1, we have:
cos(2x) = 2(24/25)^2 - 1 = 2(576/625) - 1 = 1152/625 - 1 = 1152/625 - 625/625 = 527/625.

Therefore, the value of cos(2x) is 527/625.

To find cos(2x), you can use the double angle formula for cosine: cos(2x) = 1 - 2sin^2(x).

Given that sin(x) = 7/25 and x lies in quadrant 1, we can determine that cos(x) is positive. This means that we only need to find the positive value for cos(2x).

First, let's find sin^2(x) using the given information. Since sin(x) = 7/25, we have:

sin^2(x) = (7/25)^2 = 49/625.

Now, we can substitute sin^2(x) into the double angle formula:

cos(2x) = 1 - 2(49/625).

Simplifying further:

cos(2x) = 1 - 98/625.

To add the fractions, both denominators must be the same, so we can rewrite 1 as 625/625:

cos(2x) = 625/625 - 98/625.

Now, we can subtract the fractions:

cos(2x) = (625 - 98)/625.

Simplifying the numerator:

cos(2x) = 527/625.

Therefore, the correct value for cos(2x) when sin(x) = 7/25 and x lies in quadrant 1 is 527/625.