Question

5+ 3 cos ½x = 7
how to find the x?​

Answer 1

`x=\pm 2 arcos((2)/(3))+4k\pi`

where
`k` is an integer

Explanation:

`5+3\cos((1)/(2)x)=7`

We are going to isolate the trig expression first.

Subtract 5 on both sides:

`3\cos((1)/(2)x)=2`

Divide both sides by 3:

`\cos((1)/(2)x)=(2)/(3)`

Now since
`\cos(u)` is even then
`\cos(u)=\cos(-u)`.

So we have:

`\cos((1)/(2)x)=(2)/(3)`

implies:

`(1)/(2)x=arccos((2)/(3))+2k\pi`

Multiply both sides by 2:

`x=2arccos((2)/(3))+4k\pi`

or

`-(1)/(2)x=arcos((2)/(3))+2k\pi`

Multiply both sides by -2:

`x=-2arccos((2)/(3))-4k\pi`

So we can say the solution is:

`x=\pm 2arcos((2)/(3))+4k\pi`

(
`k` is an integer)