+0  
 
0
94
3
avatar+4 

Please show steps or explain as I would like to learn how to solve future questions. Thank you :)

 Jul 24, 2022
 #1
avatar+124674 
+3

1.  Note that  sin ( x - pi)  = sin x cos (pi ) - sin( pi ) cos x  =  sinx * (-1) - 0 * cosx  =  -sin x

 

So

 

2sin ( x -pi )  - 1  = 0

 

2 (-sin x)  - 1 = 0

 

-2sin x  =  1

 

sin x  =  -1/2

 

x =   7pi / 6  + n* 2pi         and  x  = 11pi/6  + n* 2pi

 

Where n is an  integer

 

 

cool cool cool

 Jul 24, 2022
 #2
avatar+124674 
+3

2.   -3cos ( pi  - 2x)  =  1

 

Note   

 

cos (pi -2x)  =  cos (pi) cos (2x)  + sin (pi) * sin (2x)  =  -1cos (2x) + 0* sin (2x)  = -cos (2x)

 

So

 

-3 (-cos (2x) )  = 1

 

3 cos (2x)   = 1

 

cos (2x)  =  1/3

 

arccos (1/3)  = x    ≈  .123  rads 

 

So

 

2x  =  1.23

 

x = 1.23 / 2  ≈  .615 rads

 

So   x =     [ .615  + 2pi * n ] rads      where n is an integer

 

Also   

 

x = [ (2pi - .615 )   + 2pi*n] rads   ≈  [   5.668  + 2pi*n ] rads    where n is an integer

 

 

cool cool cool

 Jul 24, 2022
 #3
avatar+118117 
0

You beat me to it Chris  wink

 Jul 24, 2022

10 Online Users

avatar
avatar