# trig

• October 17th 2012, 04:05 PM
pnfuller
trig
when does sec2​x equal 4?
• October 17th 2012, 04:17 PM
MarkFL
Re: trig
Take the square root of both sides, then write in terms of cosine if that helps. What do you find?
• October 17th 2012, 04:21 PM
pnfuller
Re: trig
pi/3... 2pi/3... 4pi/3... 5pi/3
• October 17th 2012, 04:24 PM
MarkFL
Re: trig
Yes, assuming we are given $0\le x<2\pi$.
• October 17th 2012, 04:26 PM
pnfuller
Re: trig
or plus 2npi for each if not given that interval?
Quote:

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

• October 17th 2012, 07:14 PM
MarkFL
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 $k\in\mathbb{Z}$.
• October 27th 2012, 03:07 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 $\pi$, 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 $k\in\mathbb{Z}$.