Question

If sin(x) = 1/4, what is sin(2x)?
a) 1/2
b) 1/8
c) 1/16
d) 1/4

Answer 1

Using the double angle formula and the Pythagorean identity, we find that sin(2x) is not one of the provided options when sin(x) = 1/4. The correct calculation results in sin(2x) = (√15)/8, which suggests an error in the given choices.

Step-by-step explanation:

If sin(x) = 1/4, we can use the double angle formula for sine to find sin(2x). The double angle formula states that sin(2x) = 2sin(x)cos(x). Since we know sin(x), we need to find cos(x) to calculate sin(2x). To find cos(x), we use the Pythagorean identity which says sin^2(x) + cos^2(x) = 1. Plugging in our value of sin(x), we get (1/4)^2 + cos^2(x) = 1 or 1/16 + cos^2(x) = 1. Solving for cos(x), we get cos(x) = √(1 - 1/16) = √(15/16) = (√15)/4.

Now, plug sin(x) and cos(x) into the double angle formula to find sin(2x): sin(2x) = 2 * (1/4) * (√15)/4 = (√15)/8. This answer is not one of the provided options, indicating a potential issue with the question or the provided choices.