Question

Use the following to find sin 2x, cos 2x, and tan 2x. Given: cos x= 5/13, for 3 pi/2 12 years ago

Answer 1

\[\sin(2x)=2\sin(x)\cos(x)\]

Answer 2

you know \(\cos(x)=\frac{5}{13}\) but you need \(\sin(x)\)
do you know how to find it?

Answer 3

Yes I do

Answer 4

ok good, what is \(\sin(x)\) ?

Answer 5

12/13

Answer 6

careful

Answer 7

you are told at the beginning that \(x\) is in quadrant 4, so
\[\sin(x)=-\frac{12}{13}\]

Answer 8

Ok

Answer 9

that was the
\[\frac{3\pi}{2}<x<2\pi\] business at the beginning

Answer 10

Ok

Answer 11

then plug in the numbers and compute
\[\sin(2x)=2\sin(x)\cos(x)=2\times \left(-\frac{12}{13}\right)\times \left(\frac{5}{13}\right)\]

Answer 12

\[\cos(2x)=1-2\cos^2(x)=1-2\times\left(\frac{5}{13}\right)^2\] etc

Answer 13

clear more or less?

Answer 14

More

Answer 15

lol
good!