Question

5+ 3 cos ½x = 7
how to find the x?​

Answer 1

Answer:

$x=\pm 2 arcos(\frac{2}{3})+4k\pi$

where $k$ is an integer

Step-by-step explanation:

$5+3\cos(\frac{1}{2}x)=7$

We are going to isolate the trig expression first.

Subtract 5 on both sides:

$3\cos(\frac{1}{2}x)=2$

Divide both sides by 3:

$\cos(\frac{1}{2}x)=\frac{2}{3}$

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

So we have:

$\cos(\frac{1}{2}x)=\frac{2}{3}$

implies:

$\frac{1}{2}x=arccos(\frac{2}{3})+2k\pi$

Multiply both sides by 2:

$x=2arccos(\frac{2}{3})+4k\pi$

or

$-\frac{1}{2}x=arcos(\frac{2}{3})+2k\pi$

Multiply both sides by -2:

$x=-2arccos(\frac{2}{3})-4k\pi$

So we can say the solution is:

$x=\pm 2arcos(\frac{2}{3})+4k\pi$

($k$ is an integer)