Question

Solve for angle x:
cos(x/2)=1/2

Show the work.

Answer 1

Answer and Step-by-step explanation:

To solve for x, we need to get x by itself.

We start off by taking the inverse cosine of both sides of the equation.

`cos^(-1)(cos((x)/(2) )=cos^(-1)((1)/(2) )\\\\(x)/(2) =cos^(-1)((1)/(2) )`

Now, multiply both sides of the equation by 2.

`2((x)/(2) )=2(cos^(-1)((1)/(2) ))\\\\\\x=2cos^(-1)((1)/(2) )`

To simplify this further,
`cos^(-1)((1)/(2) )` is equal to
`(\pi)/(3)`.

`x = 2((\pi )/(3) )\\\\x=(2\pi )/(3)`

So the final answer is
`\\x=(2\pi )/(3)`.