SOLUTION: If sin(x) = 1/3 and sec(y) = 13/12, where x and y lie between 0 and 𝜋/2, evaluate the expression. sin(x − y)

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Question 1196621: If sin(x) = 1/3 and sec(y) = 13/12, where x and y lie between 0 and 𝜋/2,
evaluate the expression.
sin(x − y)
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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If sin(x) = 1/3 and sec(y) = 13/12, where x and y lie between 0 and 𝜋/2,
evaluate the expression sin(x − y).
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If sin(x) = 1/3 and x lies between 0 and 𝜋/2,  then  

   cos(x) = sqrt%281-sin%5E2%28x%29%29 = sqrt%281-%281%2F3%29%5E2%29 = sqrt%288%29%2F3.


If sec(y) = 13/12,  then  

   cos(y) = 1%2Fsec%28y%29 = 12/13  and  sin(y) = sqrt%281-cos%5E2%28y%29%29 = sqrt%281-%2812%2F13%29%5E2%29 = 5%2F13.


sin(x-y) = sin(x)*cos(y) - cos(x)*sin(y) = %281%2F3%29%2A%2812%2F13%29+-+%28sqrt%288%29%2F3%29%2A%285%2F13%29 = %2812-5%2Asqrt%288%29%29%2F39 = 

         = %2812-5%2A2%2Asqrt%282%29%29%2F39 = %2812-10%2Asqrt%282%29%29%2F39.        ANSWER

Solved.