+0  
 
0
85
1
avatar

Let theta be an acute angle such that sin 2 theta = sin 3 theta + sin theta.  What is the measure of theta in degrees?

 Apr 27, 2022
 #1
avatar+124598 
+1

2sinxcosx   =  sin (2x)cosx + sinxcos(2x) + sin x

 

2sin x cos x  =  2sinxcos^2x + sinx (cos^2x - sin^2x)  +  sinx

 

2sinx cos x  = 3sinxcos^2x  - sin ^3 x  +sin x

 

Since sin x    not  = 0 ,  divide through by sin x

 

2cosx  = 3cos^2x - sin^2x  + 1

 

2cosx  = 3cos^2x  - (1 - cos ^2x) + 1

 

2cos x = 4cos^2 x  

 

4cos^2x  - 2cos x  =  0

 

2cos x  ( 2cos x   - 1)  =  0

 

2cos x  =  0

cos x  = 0

x = 90°   (not acute)

 

2cos x    -1    = 0

 

2cos x = 1

 

cos x =  1/2   

 

x  =  60° =  theta

 

 

 

 

 

cool coolcool

 Apr 28, 2022

22 Online Users

avatar