mathslover
  • mathslover
sin ( 90 + theta ) = cos theta prove^
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
i guess it depends on what you can use if you can use the addition angle formula, that would work if not maybe with a triangle you can see it
mathslover
  • mathslover
i want to do with the triangle one but m wondering how will you show (90+theta) in a right angled triangle?
anonymous
  • anonymous
|dw:1350098235823:dw|

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mathslover
  • mathslover
yes but that is 90 - theta? do 90-theta has any relation with 90 + theta ?
anonymous
  • anonymous
\[\cos(x)=\frac{a}{c}=\sin(90-x)=-\sin(x-90)\] \[=\sin(x-90+180)=\sin(x+90)\]
mathslover
  • mathslover
how : -sin(x-90) = sin(x-90+180) ?
anonymous
  • anonymous
third equal sign because sine is odd, fourth because \(\sin(x)=-\sin(x+180)\)
mathslover
  • mathslover
Gotcha now, thanks a lot!
anonymous
  • anonymous
your on the other side of the unit circle |dw:1350098472701:dw|
anonymous
  • anonymous
yw
mathslover
  • mathslover
hey, how you did this step? : \[\large{-\sin(x-90) = sin(x-90+180) }\] ?
mathslover
  • mathslover
@satellite73 did you subtract sin(180) both sides?
anonymous
  • anonymous
i added 180 inside because \(\sin(x)=-\sin(x+180)\)
mathslover
  • mathslover
oh k , got it!

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