A Region Lying Between Two Intersecting Graphs

• Jan 31st 2013, 07:01 PM
asilvester635
A Region Lying Between Two Intersecting Graphs
How does tanx = 1 be pi/4 or 5pi/4?????? I'm confused
• Jan 31st 2013, 08:35 PM
ibdutt
Re: A Region Lying Between Two Intersecting Graphs
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
• Jan 31st 2013, 10:58 PM
asilvester635
Re: A Region Lying Between Two Intersecting Graphs
Tangent is a periodic function with period $\displaystyle \pi$. If, for some x and y, tan(x)= y then it is also true that $\displaystyle tan(x+ n\pi)= y$ for any integer, n. In particular, $\displaystyle tan(\pi/4)= \frac{sin(\pi/4)}{cos(\pi/4)}= \frac{\sqrt{2}/2}{\sqrt{2}/2}= 1$ so $\displaystyle tan(\pi/4+ \pi)= tan(5\pi/4)= 1$. It is also true that $\displaystyle tan(\pi/4- \pi)= tan(-3\pi/4)= 1$, that $\displaystyle tan(\pi/4+ 2\pi)= tan(9\pi/4)= 1$, and that, in general, $\displaystyle tan(\pi/4+ n\pi)= tan(((4n+1)/4)\pi)= 1$ for any integer, n.