Question

Please help! I know me have 10 minutes! Find all solutions to 20cos(2pi/5 x) = 10✔️2

Answer 1

Answer: A

Explanation:

You have:

`20cos((2\pi )/(5) x)=10√(2)`

Begin by dividing both sides by 20 to get:

`cos((2\pi )/(5) x)=(√(2) )/(2)`

Take the arccosine of both sides to get:

`arccos(cos((2\pi )/(5) x))=arccos((√(2) )/(2))`

`(2\pi )/(5) x=arccos((√(2) )/(2) )`

First of all, lets find the right side. Cosine of what gives sqrt 2 over 2? That would be pi/4, plus 2npi. Another solution would be 7pi/4, plus 2npi. We have:

`(2\pi )/(5) x=\pi /4+2n\pi`

`(2\pi )/(5) x=7\pi /4+2n\pi`

Isolate 'x' to get:

`x=(5)/(2\pi ) (\pi /4+2n\pi)=(5)/(8) +5n`

`x=(5)/(2\pi ) (7\pi /4+2n\pi)=(35)/(8) +5n`