Find all solution to the equation 3tan(x)=8/sin(x) for 0<=x<=360 degrees

By multipying across and using some trigonometric identities we can turn this in to a much simpler quatratic which can be solved using the quadratic formula. This step can be simplified by using the substitution y=cos(x). Using this we find y=1/3, -3 and hence cos(x)=1/3, -3. The latter has no real solutions as x is bounded between -1 and 1. However 1/3 gives a solution of approximately 70.5 degrees. It's important to remember the second solution of 289.5 degrees, this is due to the nature of the cosine graph and the range we have been given in the question.