SOLUTION: If sin(x) + cos(x) = 2/3, then find the value of sin(2x).

Algebra ->  Trigonometry-basics -> SOLUTION: If sin(x) + cos(x) = 2/3, then find the value of sin(2x).       Log On


   

Question 544717: If sin(x) + cos(x) = 2/3,
then find the value of sin(2x).
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Square both sides of the first equation, the result is
sin%5E2%28x%29%2B2%2Asin%28x%29%2Acos%28x%29%2Bcos%5E2%28x%29=4%2F9
%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2B2%2Asin%28x%29%2Acos%28x%29=4%2F9, use the Pythagorean Identity sin%5E2%28x%29%2Bcos%5E2%28x%29=1, the result is
1%2B2%2Asin%28x%29%2Acos%28x%29=4%2F9, use the double angle formula sin%282x%29+=+2sin%28x%29%2Acos%28x%29, the result is
1%2Bsin%282x%29=4%2F9
Therefore highlight%28sin%282x%29=-5%2F9%29