Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why -pi/2=1 and pi/2=5?

  1. Nov 20, 2014 #1
    Please take a look the below problem:

    ##\int^{π/2}_{-π/2}\frac{4cosθ}{3+sin2θ}dθ##

    ##
    u = 3 + 2 sinθ, du = 2 cosθ dθ,
    ##
    ##
    u(-π/2)=1, u(π/2)=5
    ##

    ##\int^{π/2}_{-π/2}\frac{4cosθ}{3+sin2θ}dθ=\int^{5}_{1}\frac{2}{u}du##
    ##=2ln|u|]^{5}_{1}##
    ##=2ln|5|-2ln|1|##
    ##=2ln5##

    I wonder why -pi/2 = 1 and pi/2 = 5?

    Note:
    How to insert latex?
    How do you add space in latex?
    How do you align at =?
     
  2. jcsd
  3. Nov 20, 2014 #2

    td21

    User Avatar
    Gold Member

    because sin(-pi/2) = -1 and sin(pi/2) = 1
     
  4. Nov 20, 2014 #3

    ShayanJ

    User Avatar
    Gold Member

    Well, the function [itex] u(\theta)=3+2\sin\theta [/itex] is neither even nor odd so [itex] u(\theta) [/itex] and [itex] u(-\theta) [/itex] have no relationship!

    You did insert latex!
    Just type a \ followed by a space.
    Put a & before the = and at next lines, put & where you want to be aligned with =.
     
  5. Nov 20, 2014 #4
    Why pi/2 = 5?
     
  6. Nov 20, 2014 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    pi/2 ≠ 5. It's u(π/2) = 5, where u(θ)=3+2sinθ, and sin(π/2) = 1

    You should brush up on your trigonometry before diving into calculus.
     
  7. Nov 20, 2014 #6

    mathman

    User Avatar
    Science Advisor
    Gold Member

    θ
    Your first integral has sin2θ, while the next line has 2sinθ. Which is it?
     
  8. Nov 20, 2014 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Since you asked these questions, it's nice to know how to render functions nicely: \sin x renders [itex]\sin x [/itex], to be compared to [itex] sin x[/itex]. Likewise for \ln x vs ln x.
     
  9. Nov 21, 2014 #8
    Sorry it's an error. The correct one is 2 sinθ.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why -pi/2=1 and pi/2=5?
  1. |2/3x||x-(1/2)| < A (Replies: 2)

Loading...