Need help solving: Find all the angles in terms of pi for 0 < x < 5 which satisfy,
sin 2x = sin (x - 4)
Answers ( (4-pi)/3 , (4+pi)/3, (4+3pi)/3, 2pi-4)
Thank you. jt
Originally posted by Jt061952:Need help solving: Find all the angles in terms of pi for 0 < x < 5 which satisfy,
sin 2x = sin (x - 4)
Answers ( (4-pi)/3 , (4+pi)/3, (4+3pi)/3, 2pi-4)
Thank you. jt
sin (2x) - sin (x-4) =0
Using sin A - sin B = 2cos (A+B)/2 sin (A-B)/2
2cos[(2x+x-4)/2] sin [(2x-x+4)/2] =0
2cos(1.5x-2)sin(0.5x+2)=0
cos(1.5x-2) = 0 or sin(0.5x+2)=0
For cos(1.5x-2)=0
Basic angle = pi/2 (-2<1.5x-2<5.5)
1.5x-2 = -pi/2, pi/2 or 3pi/2
3x/2 = (4-pi)/2, (4+pi)/2 or (4+3pi)/2
3x = 4-pi, 4+pi or 4+3pi
x = (4-pi)/3, (4+pi)/3 or (4+3pi)/3
For sin(0.5x+2) = 0
Basic angle = 0 (2<0.5x+2<4.5)
0.5x+2 = pi
x = 2pi-4
Thanks Mikethm, I guess my problem was using your second step shown,
sin A - sin B = 2cos (A+B)/2 sin (A-B)/2
Appreciate your help, jt