+0  
 
+1
171
1
avatar+23 

cosθ= −√3/4, where π≤ θ≤ 3π/2. tanβ= 3/4, where 0≤β≤ π/2. What is the exact value of sin(θ+β)?Enter your answer, as a fraction in simplified form

 Apr 9, 2020
 #1
avatar+111329 
+2

cos θ  =  - √3/4

So  sin θ  = -√ [ 4^2  - (-√3)^2 ] / 4  =   - √[  16  - 3 ] / 4   =  -  √13  / 4

 

tan B = 3/4

sin B = 3/5

cos B =  4/5

 

So

 

sin ( θ  + B)  =    sinθ cosB + sinBcosθ   =  

 

(-√13/4 )  * (4/5)     +  ( 3/5 ) * ( - √3/4 )  =

 

[ -4√13  -  3√3 ]

______________

         20

 

 

cool cool cool

 Apr 9, 2020

12 Online Users

avatar
avatar