SOLUTION: If sin x= 0.8 and sin y = 0.6, calculate sin (x+y) without use of a calculator

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Question 1111801: If sin x= 0.8 and sin y = 0.6, calculate sin (x+y) without use of a calculator
Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
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Since  sin(x) = 0.8,  then  cos(x) = sqrt%281-sin%5E2%28x%29%29 = sqrt%281-0.8%5E2%29 = sqrt%281-0.64%29 = sqrt%280.36%29 = 0.6   (assuming x is acute angle).


Since  cos(y) = 0.6,  then  sin(y) = sqrt%281-cos%5E2%28y%29%29 = sqrt%281-0.6%5E2%29 = sqrt%281-0.36%29 = sqrt%280.64%29 = 0.8   (assuming y is acute angle).


Then

sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y) = 0.8*0.6 + 0.6*0.8 = 0.48 + 0.48 = 0.96.

Solved.