Question

Please help, thank you!

Find the exact value:
cos Ф=3/5 where 270≤Ф<360
find cos2Ф

Answer 1

-7/25

Explanation:

Disclaimer: I'm using variable x instead of theta.

Step 1: Simplify cos 2x.

`\cos(2x) = \cos {}^(2) (x) - { \sin {}^(2) (x) }^(2)`

`\cos(2x) = \cos {}^(2) (x) - (1 - \cos {}^(2) (x) )`

`2 \cos {}^(2) (x) - 1`

We know that cos x= 3/5 so that means

`2((3)/(5) ){}^(2) - 1 = 2( (9)/(25) ) - 1 = (18)/(25) - 1 = ( - 7)/(25)`

So the exact value of cos 2x=

`( - 7)/(25)`

There is another way to find this but this is easier.

Answer 2

`cos2\theta = -frac7{25}`

Explanation:

By using the double angle formula for cosine
`cos 2\theta = 2cos^2\theta -1`, replacing the value we have we get

`cos 2\theta = 2 (\frac35)^2 -1 = 2\frac9{25} -1 = (18)/(25)-(25)/(25) = -(7)/(25)`