Posted by
**Edward** on
.

Solve this equation fo rx in the interval 0<=x<=360

3sinxtanx=8

I would do it this way:

sinxtanx = 8/3

sinx(sinx/cosx)=8/3

sin^2x/cosx = 8/3

(1-cos^2x)/cosx=8/3

cross-multiply

3 - 3cos^2x = 8cosx

3cos^2x + 8cosx - 3 = 0

(3cosx-1)(cosx+3)=0

cosx=1/3 or cosx = -3

the last one is not possible

so x = arccos(1/3)=70.5º

or 289.5º (in the fourth quadrant)