moongazer
  • moongazer
Why is it the sine of an angle is also equal to the sine of 180 minus that angle ? e.g. sin 45degrees = sin 135degrees
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Because the elevation of the inscribed triangle (to the unit circle) is still positive.
moongazer
  • moongazer
I also noticed that.
anonymous
  • anonymous
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moongazer
  • moongazer
but why "180 - angle", not "angle - 180"
anonymous
  • anonymous
Well, in the given example. If angle = 45, then 45 - 180 = -90. sin(-90) is not equal to sin(45)
anonymous
  • anonymous
Sorry, the calculation was wrong there. 45 - 180 = -135. But the same applies, sin(-135) is not equal to sin (45)
anonymous
  • anonymous
It would have the same *magnitude* but not the same *sign*.
moongazer
  • moongazer
I already understand that the value of sine in Q1 is also equal to the sine in Q2. but where did you get the 180- angle like how did you get the lwh for volume
anonymous
  • anonymous
Well, volume doesn't come into question here. But it's a simple matter of the definition of the "sine" function. 180 - 45 = 135, and when you have 45 and 135....the inscribed triangle's elevation is equal in both magnitude and sign.
anonymous
  • anonymous
If you go the other direction, you get opposed angles (pointing opposite directions). So you'll get an elevation equal in magnitude but NOT equal in sign.
moongazer
  • moongazer
ohh ok thanks :)
anonymous
  • anonymous
np.
moongazer
  • moongazer
so "sin(180-angle)" is equal to "angle" because "180-angle" always give an angle that is equal to the sine of the "angle". is it like that ?
moongazer
  • moongazer
anonymous
  • anonymous
Well, because the way sine is DEFINED. Remember SOHCAHTOA. Sin = Opp/Hyp Hypotenuse is always positive. So you're looking at the opposite leg of a triangle. The elevations must both have the same sign, if they do not...then the sine's will not match.
moongazer
  • moongazer
ok, thanks again :)
anonymous
  • anonymous
np.

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