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M$1 March 18, 2009 09:46 PM

when im working out the answers to trig questions how do i find out the rest of the answers

for example arcsin(4/5) first answer is 53.1, how do i find the other answers?
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March 18, 2009 10:36 PM
SOH- CAH - TOA (phonetically : so-ka-towa)

Sin = Opposite/Hypotenuse
Cosin = Adjacent/Hypotenuse
Tan = Opposite/Adjacent

http://calc101.com/webMathematica/derivatives.jsp
http://mathforum.org/library/drmath/view/54137.html
http://library.thinkquest.org/20991/alg2/eqtri.html

That's the basis of how I remember all this stuff!


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March 19, 2009 12:16 AM
Arcsin is usually defined for the range of -90 to 90, but if you want to find it for all real numbers, subtract your first answer from 180. The answer for all real numbers is now first answer + N360, where N is an integer, and your second answer where N360, where N is an integer.
For example:
Arcsin(1/2)=30
Second answer=180-30=150
So for all real numbers, Arcsin(1/2)= 30+N360, 150+N360, where N is an integer. You can try with different values of N to see that this works.

For Arccos, the idea is the same except you subtract from 360, instead of 180.
E.g. arccos(1/2)=60+N360, 300+N360, where N is an integer.

Note: If you are using these in the context of a triangle, make sure to only use values that are less than 180.

Is that what you meant by the other answers? If not, just comment.

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