# trig

• Oct 17th 2012, 03:05 PM
pnfuller
trig
when does sec2​x equal 4?
• Oct 17th 2012, 03:17 PM
MarkFL
Re: 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 PM
pnfuller
Re: trig
pi/3... 2pi/3... 4pi/3... 5pi/3
• Oct 17th 2012, 03:24 PM
MarkFL
Re: trig
Yes, assuming we are given $\displaystyle 0\le x<2\pi$.
• Oct 17th 2012, 03:26 PM
pnfuller
Re: trig
or plus 2npi for each if not given that interval?
Quote:

Originally Posted by MarkFL2
Yes, assuming we are given $\displaystyle 0\le x<2\pi$.

• Oct 17th 2012, 06:14 PM
MarkFL
Re: 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 AM
Kyood
Re: trig
Quote:

Originally Posted by MarkFL2
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 $\displaystyle k\in\mathbb{Z}$.