Math Question: 12csc^3 theta -48csc theta =0 please solve all values of theta writhing [0,2pie)

I will use x instead of theta 12(cscx)^3 - 48cscx = 0 Factor this and set each factor equal to zero: 12cscx ((cscx)^2 - 4) = 0 cscx = 0 or (cscx)^2 = 4 cscx = 0 has no solutions (cscx)^2 = 4 implies cscx = 2 or cscx = -2 So, sinx = 1/2 or sinx = -1/2 sinx = 1/2 implies x = pi/6 or 5pi/6 sinx = -1/2 implies x = 7pi/6 or 11pi/6 So, the solutions are: x = pi/6, 5pi/6, 7pi/6, 11pi/6 All of the pi/6's one trip around the unit circle!
Answered On 04/25/2020 01:14