Question 607037
Use the double-angle formulas.


*[tex \LARGE \sin (2x) = 2 \sin x \cos x]


Here you need to find cos x. Since sin x = 7/8 and *[tex \LARGE \sin^2 x + \cos^2 x = 1] then *[tex \LARGE (\frac{7}{8})^2 + \cos^2 x = 1 \Rightarrow \cos x = \frac{\sqrt{15}}{8}] (note that cos x > 0)


Plug everything in to obtain *[tex \LARGE \sin (2x) = \frac{7\sqrt{15}}{32}]


Finding cos x is fairly simple. Use the identity *[tex \LARGE \cos (2x) = 1 - 2 \sin^2 x] and replace sin x with 7/8.


Finding tan x is even simpler. Since tan x = (sin x)/(cos x), use the results you found in the previous two parts to find tan x.