trig equation (1 Viewer)

[philly2000]

cos(4x) - 7sin^2 (2x) = 0 solve for 0 =< x =< 360

thanks

 

[Drongoski]

cos 4x - 7 sin²2 x = 0

.: (1 - 2sin²2x) - 7 sin²x = 0

i.e. 1 - 9 sin²2x = 0

i.e. (1-3sin 2x)(1 + 3sin 2x) = 0

.: either (1): 1 - 3sin 2x = 0 ==> sin 2x = 1/3

or (2): 1 + sin 2x = 0 ==> sin 2x = -1/3

For (1): 2x = 19.5, 160.5, 369.5, 520.5 deg.

For (2): 2x = 199.5, 340.5, 559.5, 700.5 deg

For x, just divide by 2

 

[study-freak]

For a nice looking solution

 

[philly2000]

gah thanks guys, cant believe i couldnt see that >->'