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Further Trigonometry

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the values of the following, without the use of a calculator,
    cos(15)+sin(15)


    2. Relevant equations
    sin(A±B)= sinAcosB±cosAsinB
    cos(A±B)= cosAcosB∓sinAsinB

    3. The attempt at a solution
    Without the use of a calculator i had to relate back to the 2 triangles which you get the most common values for sin, cos and tan. Namely,
    sin(30)= 1/2
    cos(30)= √3/2
    sin(45)= 1/√2
    cos(45)= 1/√2
    sin(60)= √3/2
    cos(60)= 1/2
    sin(0)= 0
    cos(0)= 1
    sin(90)=1
    cos(90)= 0
    but i have found no use for any of these, also i didnt think tan was appropriate but im open to correction!! i tried going along the lines of gettting a trig function, with the same angle, to equal 1 so i could use the addition formulae but i had no success!
    any help please guys!!
     
  2. jcsd
  3. Feb 25, 2009 #2

    Mark44

    Staff: Mentor

    The double angle formulas for cosine can be manipulated to give half-angle formulas.
    cos(2a) = cos^2(a) - sin^2(a) = 1 - 2sin^2(a) = 2cos^2(a) - 1
    ==> cos(a) = 1 - 2sin^2(a/2) and cos(a) = 2cos^2(a/2) - 1

    Take the last two equations and solve for cos(a/2) in one and sin(a/2) in the other.
     
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