SOLUTION: Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.) cos x = sqrt(2)/7 ,3&#960;/2 < x < 2&#960; a)cos 2x b)sin 2x c)tan 2

Algebra ->  Trigonometry-basics -> SOLUTION: Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.) cos x = sqrt(2)/7 ,3&#960;/2 < x < 2&#960; a)cos 2x b)sin 2x c)tan 2      Log On


   



Question 737549: Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.)
cos x = sqrt(2)/7 ,3π/2 < x < 2π
a)cos 2x
b)sin 2x
c)tan 2x
I know that for cos 2x, the answer will be #/49 but that is really as far as I got

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.)
cos x = sqrt(2)/7 ,3π/2 < x < 2π
a)cos 2x
b)sin 2x
c)tan 2x
***
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
cos%28x%29=sqrt%282%29%2F7=A%2FH
A=sqrt%282%29%2C+H=7
O=sqrt%28H%5E2-A%5E2%29=sqrt%2849-2%29=sqrt%2847%29
sin%28x%29=O%2FH=sqrt%2847%29%2F7
tan%28x%29=O%2FA=sqrt%2847%29%2Fsqrt%282%29
...
cos%282x%29=cos%5E2%28x%29-sin%5E2%28x%29=%282%2F49%29-%2847%2F49%29=-45%2F49
sin%282x%29=2sin%28x%29cos%28x%29=2%2Asqrt%2847%29%2F7%2Asqrt%282%29%2F7=2sqrt%2894%29%2F49