MHB Find x (Radians): Solve sec(2π/3 + x) = 2

[eleventhxhour]

If sec(2pi/3 + x) = 2, what does x equal?

So far I changed it to cos by dividing 1/2. And then, I changed the 1/2 to radians which is pi/3. But, I'm not sure what to do next.

 

[MarkFL]

If you are going to find the general solution, you could write:

$$x+\frac{2\pi}{3}=2k\pi\pm\frac{\pi}{3}$$

And then solve for $x$. :D

 

[Maged Saeed]

Also you can do it using your way

$$sec(\frac{2\pi}{3}+x)=2$$

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

then

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

$$\frac{2\pi}{3}+x=kx\pi \pm \frac{\pi}{3}$$

solve for x now ..

:)

 

[MarkFL]

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

$$\frac{2\pi}{3}+x=kx\pi \pm \frac{\pi}{3}$$

...

How does that follow?

 

[Maged Saeed]

How does that follow?

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

$$cos^{-1}cos(\frac{2\pi}{3}+x)=cos^{-1}(\frac{1}{2})$$

$$\frac{2\pi}{3}+x=\frac{\pi}{3}$$

To here , I think I'm correct because the range of arc-cos function is
from zero to PI.
But cannot we expand it to be (2xPI + PI/3) "the solution set of cos function"?

I'm not sure

(Thinking)