Question

If cos 2x = 7/8 find sin x

• A. $\pm 1/4$
• B. $\pm 1/\sqrt{2}$
• C. $\pm 1/\sqrt{8}$
• D. $\pm 1/2$

Answer 1

Answer: (A)

$\pm 1/4$

Answer 2

We are given that $\cos 2x = \frac{7}{8}$ and we want to find $\sin x$. We can use the double angle identity $\cos 2x = 1 - 2\sin^2 x$. Substituting the given value, we have:

$\frac{7}{8} = 1 - 2\sin^2 x$

Rearranging the equation to solve for $\sin^2 x$:

$2\sin^2 x = 1 - \frac{7}{8} = \frac{1}{8}$

$\sin^2 x = \frac{1}{16}$

Taking the square root of both sides:

$\sin x = \pm \sqrt{\frac{1}{16}} = \pm \frac{1}{4}$

Therefore, $\sin x = \pm \frac{1}{4}$.