Question

Use the following to find sin2x, cos2x, and tan2x Given: cos x = 7/25, for 3pi/2 12 years ago

Answer 1

\(\bf cos(x)=\cfrac{7}{25}\implies \cfrac{adjacent}{hypotenuse}\implies \cfrac{a=7}{c=25}\\ \quad \\
\textit{using the pythagorean theorem }c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}={\color{blue}{ b}}\)

once you find "b", then you'd have all sides of the angle
use that to get the identities

Answer 2

x lies in 4 th quadrant.
sinx and tan x are negative.

sin 2x=2sin x cos x=?
\[\cos2x=\sqrt{1-\sin ^{2}(2x)}\]
\[\tan 2x=\frac{ \sin 2x }{ \cos 2x }=?\]
or you can find tan 2x this way.
\[\tan 2x=\frac{ 2\tan x }{ 1-\tan ^{2}x }\] =?

Answer 3

Thank you

Answer 4

yw