SOLUTION: Find the exact value. Do not use a calculator. sin(-15π) = ___________ I have searched my book for examples on how to work this problem and I'm having a hard time find

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value. Do not use a calculator. sin(-15π) = ___________ I have searched my book for examples on how to work this problem and I'm having a hard time find      Log On


   

Question 402407: Find the exact value. Do not use a calculator.
sin(-15π) = ____________

I have searched my book for examples on how to work this problem and I'm having a hard time finding a solution or an example of how to find the answer..If you could help me that would be great! Thanks!
Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
angles greater than 2π (360º) just repeat the reference circle over (and over) again

-15π is 7.5 complete circles in the negative (clockwise) direction

so the reference angle is halfway around the circle; π radians or 180º

sin(180º) = ?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you went around a complete circle in a clock-wise
direction, which is (-) direction, once around is -2pi
You are back where you started at 0pi
Now suppose you do this 7 times. You have gone
around the circle -14pi times, and you are back
where you started at 0pi. Now head in the (-)
direction (CW) -pi more. That puts you at -pi
on the circle. Now the answer is sin%28-pi%29+=+0
Note that any odd number times -pi will put you
at -pi.
Hope this helps