SOLUTION: Find the exact value of cos(pi) cos(3pi/4) + sin(pi) sin (3pi/4)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of cos(pi) cos(3pi/4) + sin(pi) sin (3pi/4)      Log On


   

Question 1036513: Find the exact value of cos(pi) cos(3pi/4) + sin(pi) sin (3pi/4)
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We'll use the trig identity
cos%28X%29+cos%28Y%29+%2B+sin%28X%29+sin+%28Y%29+=+cos%28X-Y%29


cos%28pi%29+cos%283pi%2F4%29+%2B+sin%28pi%29+sin+%283pi%2F4%29+=+cos%28pi-3pi%2F4%29

cos%28pi%29+cos%283pi%2F4%29+%2B+sin%28pi%29+sin+%283pi%2F4%29+=+cos%284pi%2F4-3pi%2F4%29 use the trig identity (see above)

cos%28pi%29+cos%283pi%2F4%29+%2B+sin%28pi%29+sin+%283pi%2F4%29+=+cos%28pi%2F4%29

cos%28pi%29+cos%283pi%2F4%29+%2B+sin%28pi%29+sin+%283pi%2F4%29+=+%28sqrt%282%29%29%2F2 use the Unit Circle


The final answer is %28sqrt%282%29%29%2F2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the exact value of cos(pi) cos(3pi/4) + sin(pi) sin (3pi/4)
This represents the COSINE Difference of 2 angles, as follows: cos+%28A+-+B%29+=+cos+%28A%29+cos+%28B%29+%2B+sin+%28A%29+sin+%28B%29