Trig adding/subtracting and double angle formulas help

[Ishtar]

i am so lost in this area and have huge test coming up on tuesday
and we don't have books for this unit either so i can't 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 a lot but couldn't find websites that would explain this easily
thx

 

[HallsofIvy]

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)?

 

[Ishtar]

thx
i know formulas for sin 2x and cos 2x
sin 2x = 2sinxcosx
we never really did 1/2 angle only double angle formulas

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also we won't 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 a lot 4 ur help

also any websites will be help full too

 

[rock.freak667]

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)

 

[rocomath]

Trigonometric Identities - http://www.mathlinks.ro/weblog_entry.php?t=175270&sid=d364b3036ea21846acd82fbafe397137