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What is the exact value of sin(θ+β)? Give your answer as a simplified fraction.

 May 3, 2020
 #1
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sin (A + B)  =  sin AcosB  + sin B cos A

 

sin A  =  - sqrt  ( 3^2  - (sqrt 2)^2 )  / 3  =  - sqrt (9 - 2)  /3  = -sqrt (7) /3

 

sin B  =  4/5       cos B    =  3/5

 

So we have

 

[-sqrt (7) / 3]   *  [ 3 / 5  ]   +    [4 / 5] * [ - sqrt (2) / 3 ]   =

 

-3sqrt (7)  - 4sqrt (2)

_________________

           15

 

 

cool cool cool

 May 3, 2020

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