SOLUTION: Sin x = 1/3 ,0 < x < pi/2 Cos y = 2/5 ,0 < x < pi/2 Find sin (x+y)

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Question 989696: Sin x = 1/3 ,0 < x < pi/2
Cos y = 2/5 ,0 < x < pi/2
Find sin (x+y)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the addition formula for sines:

sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y)     (1)

(see for example the lessons  FORMULAS FOR TRIGONOMETRIC FUNCTIONS  and  Addition and subtraction formulas  in this site,
or any systematic textbook in Trigonometry).

Notice that,  since  sin(x) = 1%2F3,  cos(x) = sqrt%281-%281%2F3%29%5E2%29 = sqrt%281+-+%281%2F9%29%29 = sqrt%28%288%2F9%29%29 = 2%2F3.sqrt%282%29.

Also notice that,  since  cos(y) = 2%2F5,  sin(y) = sqrt%281+-+%282%2F5%29%5E2%29 = sqrt%281+-+%284%2F25%29%29 = sqrt%2821%2F25%29 = 1%2F5.sqrt%2821%29.

Now substitute these expressions into the formula  (1).

Good luck.