Homework Help: Trigonometry Problem

Based on your entry for #2, relevant equations, what do you know about the lowest value of the quadratic function? What is the range of 2sinx? As to mfb's point, these may be inconsistent.

 

This equation has a transcendental function equal to a polynomial. In general, there is no simple way to solve such problems. You will need to use a numerical method. (Such equations can be solved using "Lambert's W function" which is defined as the inverse function to [itex]xe^x[/itex] but converting sine to exponentials will introduce complex numbers so I would not be inclined to try that.)