Find the general solution, in degrees, of the equation 2 sin(3x+45°)= 1

A general way of solving these equations is getting them to the form sin(y)=k. In this case, to do so, we have to divide by 2 and then put y=3x+45° We then get sin(y)=1/2. You should know which angles have sine equal to 1/2: those are 30° and 150°.However, be careful: you have to write the solution including the fact that the sine is periodic! So the general solution is y= 30° + k360°, y=150°+k360°, for every integer value of k. Now we just remember what y was, and solve the equation for x. We get 3x+45° = 30°+k360° x = -5° + k120° = 115° + k120° and x=35°+k 120°. Usually, it is a good habit to write separately all the solutions lying in the interval [0°, 360°], and in this case those are x=35°,115°,155°,235°,275°,355°.