A Region Lying Between Two Intersecting Graphs

**asilvester635** · January 31st 2013, 07:01 PM

How does tanx = 1 be pi/4 or 5pi/4?????? I'm confused

**ibdutt** · January 31st 2013, 08:35 PM

tan x = 1, tangent is positive in first and third quadrant. Hence the tan x will be 1 for x = pi/4 ans pi + pi/4 = 5pi/4

**asilvester635** · January 31st 2013, 10:58 PM

Don't get your explanation

**ibdutt** · February 1st 2013, 04:39 AM

Your query was as to how does tanx = 1 lead to x = pi/4 and 5pi/4
The reason for the same has been explained. tan pi/4 = 1 as well as tan 5pi/4 = 1 therefore x = pi/4 and 5pi/4 between 0 to 2pi. I hope now it is clear.

**HallsofIvy** · February 1st 2013, 07:34 AM

Tangent is a periodic function with period $\pi$ . If, for some x and y, tan(x)= y then it is also true that $tan(x+ n\pi)= y$ for any integer, n. In particular, $tan(\pi/4)= \frac{sin(\pi/4)}{cos(\pi/4)}= \frac{\sqrt{2}/2}{\sqrt{2}/2}= 1$ so $tan(\pi/4+ \pi)= tan(5\pi/4)= 1$ . It is also true that $tan(\pi/4- \pi)= tan(-3\pi/4)= 1$ , that $tan(\pi/4+ 2\pi)= tan(9\pi/4)= 1$ , and that, in general, $tan(\pi/4+ n\pi)= tan(((4n+1)/4)\pi)= 1$ for any integer, n.

**asilvester635** · February 1st 2013, 09:54 AM

Oh I get it now.. THANKS!!!!!!!

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