SOLUTION: Given: 0º < x < 90º and sin(x) = 3/5. Find the exact value of cos(x + 180º).

Algebra ->  Trigonometry-basics -> SOLUTION: Given: 0º < x < 90º and sin(x) = 3/5. Find the exact value of cos(x + 180º).      Log On


   

Question 746152: Given: 0º < x < 90º and sin(x) = 3/5.
Find the exact value of cos(x + 180º).
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
If we don't remember how phase shifts work we can always use the sum/difference identities:
cos%28x+%2B+180%29=cos%28x%29cos%28180%29-sin%28x%29sin%28180%29
now
cos(180)=-1 and sin(180)=0

cos%28x+%2B+180%29=cos%28x%29%2A%28-1%29-sin%28x%29%2A%280%29

cos%28x+%2B+180%29=-cos%28x%29

and in our case

cos%28x%29=sqrt%281-sin%28x%29%5E2%29=sqrt%281-%283%2F5%29%5E2%29=4%2F5

so

cos%28x+%2B+180%29=-4%2F5