SOLUTION: Suppose C(s) = (0.6, 0.8). Find sin (s+Π). I tried drawing a triangle with those coordinates, and I only confused myself more. Please help.

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose C(s) = (0.6, 0.8). Find sin (s+Π). I tried drawing a triangle with those coordinates, and I only confused myself more. Please help.      Log On


   

Question 818897: Suppose C(s) = (0.6, 0.8). Find sin (s+Π).
I tried drawing a triangle with those coordinates, and I only confused myself more. Please help.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm guessing that "II" means pi. In the future, just type "pi".

Using sin(A+B) = sin(A)cos(B) + cos(A)sin(B) on sin%28s%2Bpi%29 we get:
sin%28s%29cos%28pi%29%2Bcos%28s%29sin%28pi%29
Since cos%28pi%29+=+-1 and sin%28pi%29+=+0:
sin(s)(-1) + 0
which is simply:
-sin(s)

The triangle you drew should help at this point. Use the Pythagorean Theorem to find the hypotenuse:
0.6%29%5E2%2B%280.8%29%5E2+=+h%5E2
0.36+%2B+0.64+=+h%5E2
1+=+h%5E2
1+=+h

One way to look at sin is that it is y/h. So sin(s) = 0.8/1 = 0.8. This makes -sin(s):
-0.8