1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cos(45 - v) = sin (v + 45) for all angles v?

  1. Oct 11, 2004 #1
    How can I prove that
    cos(45 - v) = sin (v + 45) for all angles v? :uhh:
     
  2. jcsd
  3. Oct 11, 2004 #2
    expand LHS using cos(A-B) formula
    expand RHS using sin(A+B) formula
    show that they are equivalent

    -- AI
     
  4. Oct 11, 2004 #3
    or use the fact that cos(x) = sin(90°-x).

    ofcourse if you wanna prove the above relation you will have to follow to advice of TenaliRaman.

    regards
    marlon
     
  5. Oct 11, 2004 #4
    can one of you show me? I don`t really knowwhere to begin? :shy:
     
  6. Oct 11, 2004 #5

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    You have, cos(45° - v) = sin (v + 45°)

    Now as said before you should be aware of the relationship, cos(x) = sin(90°-x). All you have to do with this is let x = 45° - v.

    However if you work is in context of the addition of angles then:

    [tex]\sin (A \pm B) = \sin A \cos B \pm \sin B \cos A[/tex]

    [tex]\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B[/tex]

    Let A = 45° and B = v.
     
  7. Oct 11, 2004 #6
    so then I get:
    sin(45+v) = sin 45 cos v + sin v cos 45
    cos(45-v) = cos 45 cos v + sin 45 sin v

    does this prove that cos(45-v) = sin(v+45)?
     
  8. Oct 11, 2004 #7

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    Almost, what does cos 45° and sin 45° equal?
     
  9. Oct 11, 2004 #8
    0,7071?

    So I don`t have to write more that this?

    I don`t really think I`ve got it yet..
     
    Last edited by a moderator: Oct 11, 2004
  10. Oct 11, 2004 #9

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    Correct me if I am wrong but both cos 45° and sin 45° are [tex]\frac{\sqrt{2}}{2}[/tex]

    Therefore:

    [tex]\sin (45+v) = \frac{\sqrt{2}}{2} \cos v + \frac{\sqrt{2}}{2} \sin v [/tex]
    [tex]\cos (45-v) = \frac{\sqrt{2}}{2} \cos v + \frac{\sqrt{2}}{2} \sin v[/tex]

    Spot something simmilar? When proving things never ever ever ever ever ever ever ever ever ever ever ever round things off!
     
  11. Oct 12, 2004 #10
    I didn`t know that.. thanks a lot..
     
  12. Oct 12, 2004 #11

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    It's easier with sin(x) = cos(x-90).
    cos(45-v)=cos(v-45) since the cosine is even.
    cos(v-45)=sin(v+90-45)=sin(v+45)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?