## moongazer 3 years ago 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

1. qpHalcy0n

Because the elevation of the inscribed triangle (to the unit circle) is still positive.

2. moongazer

I also noticed that.

3. qpHalcy0n

|dw:1348381225832:dw|

4. moongazer

but why "180 - angle", not "angle - 180"

5. qpHalcy0n

Well, in the given example. If angle = 45, then 45 - 180 = -90. sin(-90) is not equal to sin(45)

6. qpHalcy0n

Sorry, the calculation was wrong there. 45 - 180 = -135. But the same applies, sin(-135) is not equal to sin (45)

7. qpHalcy0n

It would have the same *magnitude* but not the same *sign*.

8. 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

9. qpHalcy0n

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.

10. qpHalcy0n

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.

11. moongazer

ohh ok thanks :)

12. qpHalcy0n

np.

13. 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 ?

14. moongazer

@qpHalcy0n

15. qpHalcy0n

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.

16. moongazer

ok, thanks again :)

17. qpHalcy0n

np.