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cos theta = -sqrt2/3 , where pi is less than or equal to theta which is less than or equal to 3pi/2

tan beta = 4/3 , where 0 is less than or equal to beta which is less than or equal to pi/2

 

what is the exact value of sin ( theta + beta ) ?

 

final answer must be in a simplified fraction

 Mar 28, 2020
 #1
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Let  A  be  the first "theta"

A  is  in the  3Q  ......so the  sine  is negative  and is given by   -√  [ 3^2 - (√2)^2]  / 3  =

- √7 / 3

 

Let B  be  the  second "theta"

B is in the 1Q     and r  =  5

sin B  = 4/5       cos B =  3/5

 

sin ( A + B)  =   sin A  cos B  + sin Bcos A   =

 

(-√7/3) ( 3/5)  +  (4/5) ( -√2/3)   =

 

[  -3√7    - 4√2 ]  /   15

 

 

cool cool cool

 Mar 28, 2020

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