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Trig adding/subtracting and double angle formulas help

  1. Nov 25, 2007 #1
    i am so lost in this area and have huge test coming up on tuesday
    and we dont have books for this unit either so i cant study or look at examples for that
    i was wondering if you guys could find me website(s) which shows how to solve equations like these:

    find exact values:
    sin 67.5 degrees

    i looked alot but couldnt find websites that would explain this easily
  2. jcsd
  3. Nov 25, 2007 #2


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    Staff Emeritus
    Science Advisor

    67.5 degrees? the first thing I would do is subtract from 90: 90- 67.5= 22.5 or subtract 45 from it: 67.5- 45= 22.5. Now that's interesting! 22.5= 45/2, of course so sin(67.5)= sin(45+ 45/2) or sin(67.5)= sin(90- 45/2). Okay, what are the "sum and difference formulas" for sin? And, of course, you will need the 1/2 angle formulas. Do you know a formula for sin(x/2) or cos(x/2)?
  4. Nov 25, 2007 #3
    i know formulas for sin 2x and cos 2x
    sin 2x = 2sinxcosx
    we never really did 1/2 angle only double angle formulas


    also we wont be allowed calculators on our test and we will only be dealing with radians
    thats what i need help in is how to convert 67.5 into radians quickly

    i know that you have to divide 67.5 by 180 to get radian value but say if i get a huger number like 657 and have to convert to radians without a calculator how would i do tat

    thanks alot 4 ur help

    also any websites will be help full too
  5. Nov 25, 2007 #4


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    Homework Helper

    Well the half angle formulas are very easy to make it is simply replacing the x by x/2
    e.g. if sin2x=2sinxcosx then sinx=2sin(x/2)cos(x/2)
  6. Nov 25, 2007 #5
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