when does sec^{2}x equal 4?

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- Oct 17th 2012, 03:05 PMpnfullertrig
when does sec

^{2}x equal 4? - Oct 17th 2012, 03:17 PMMarkFLRe: trig
Take the square root of both sides, then write in terms of cosine if that helps. What do you find?

- Oct 17th 2012, 03:21 PMpnfullerRe: trig
pi/3... 2pi/3... 4pi/3... 5pi/3

- Oct 17th 2012, 03:24 PMMarkFLRe: trig
Yes, assuming we are given $\displaystyle 0\le x<2\pi$.

- Oct 17th 2012, 03:26 PMpnfullerRe: trig
- Oct 17th 2012, 06:14 PMMarkFLRe: trig
We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\displaystyle \pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:

$\displaystyle x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $\displaystyle k\in\mathbb{Z}$. - Oct 27th 2012, 02:07 AMKyoodRe: trig