SOLUTION: Find: sin(π/8)cos(π/8). Show your calculation.

Algebra ->  Trigonometry-basics -> SOLUTION: Find: sin(π/8)cos(π/8). Show your calculation.      Log On


   

Question 1105436: Find: sin(π/8)cos(π/8). Show your calculation.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28pi%2F8%29cos%28pi%2F8%29

Use the identity 

sin%282theta%29%22%22=%22%222sin%28theta%29cos%28theta%29

Swap sides:

2sin%28theta%29cos%28theta%29%22%22=%22%22sin%282theta%29

Multiply both sides by 1/2

sin%28theta%29cos%28theta%29%22%22=%22%22expr%281%2F2%29sin%282theta%29

Substitute pi%2F8 for theta

sin%28pi%2F8%29cos%28pi%2F8%29%22%22=%22%22expr%281%2F2%29sin%282%2Aexpr%28pi%2F8%29%29

sin%28pi%2F8%29cos%28pi%2F8%29%22%22=%22%22expr%281%2F2%29sin%28pi%2F4%29

And we know from the unit circle or special angles,
that sin%28pi%2F4%29%22%22=%22%22sqrt%282%29%2F2.  So:

sin%28pi%2F8%29cos%28pi%2F8%29%22%22=%22%22expr%281%2F2%29expr%28sqrt%282%29%2F2%29

sin%28pi%2F8%29cos%28pi%2F8%29%22%22=%22%22sqrt%282%29%2F4%29

Edwin