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cosθ=−√2/3 , where π≤θ≤3π/2 .

tanβ=4/3 , where 0≤β≤π/2 .

What is the exact value of sin(θ+β) ?

Give your answer as a fraction in simplified form.

 Apr 30, 2020
 #1
avatar+111435 
+1

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

 

cos A  =  −√2/3

sin A  =  - √ ( 3^2 - (√2)^2 )  / 3   =   - √ [9 - 2] / 3  =  - √7 / 3

 

tan B  =  4/3

cos B  =   3 / sqrt (3^2 + 4^2)  = 3 / sqrt 25  =  3/5

sin B  =  4/sqrt (3^2 + 4^2) = 4 /sqrt 25  =  4/5

 

So  we have 

 

sin (A + B)  = ( -√7 / 3) (3/5)  + (4/5) (-√2 / 3)  =

 

-3√7 - 4√2                 -  [ 3√7 + 4√2 ]

___________   =    ______________

       15                              15

 

 

cool cool cool

 Apr 30, 2020
 #2
avatar+25478 
+1

cosθ=−√2/3 , where π≤θ≤3π/2 .

tanβ=4/3 , where 0≤β≤π/2 .

What is the exact value of sin(θ+β) ?

Give your answer as a fraction in simplified form.

 

Answer see: https://web2.0calc.com/questions/pls-help_130#r1

 

laugh

 Apr 30, 2020

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