# Math Help - trig

1. ## trig

when does sec2​x equal 4?

2. ## Re: trig

Take the square root of both sides, then write in terms of cosine if that helps. What do you find?

3. ## Re: trig

pi/3... 2pi/3... 4pi/3... 5pi/3

4. ## Re: trig

Yes, assuming we are given $0\le x<2\pi$.

5. ## Re: trig

or plus 2npi for each if not given that interval?
Originally Posted by MarkFL2
Yes, assuming we are given $0\le x<2\pi$.

6. ## Re: trig

We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:

$x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $k\in\mathbb{Z}$.

7. ## Re: trig

Originally Posted by MarkFL2
We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:

$x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $k\in\mathbb{Z}$.