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Math Help - A Region Lying Between Two Intersecting Graphs

  1. #1
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    A Region Lying Between Two Intersecting Graphs

    How does tanx = 1 be pi/4 or 5pi/4?????? I'm confused
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    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
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    Re: A Region Lying Between Two Intersecting Graphs

    Don't get your explanation
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    Re: A Region Lying Between Two Intersecting Graphs

    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.
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  5. #5
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    Re: A Region Lying Between Two Intersecting Graphs

    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.
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    Re: A Region Lying Between Two Intersecting Graphs

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