Question 1180791
equation is 3sin^2(theta) + 2sin(theta) = 0
factor out sin(theta) to get:
sin(theta) * (3sin(theta) + 2) = 0
this is true when sin(theta) = 0 or 3sin(theta) + 2 = 0
solve for sin(theta) to get:
sin(theta) = 0 or sin(theta) = -2/3.
the reference angle (equivalent angle in the first quadrant) will be:
theta = arcsin(0) = 0 degrees.
theta = arcsin(2/3) = 41.8103149 degrees.
note that the trig function is always positive in the first quadrant.
sin(theta) is 0 when theta = 0 or 180 degrees or 360 degrees.
sin(theta) is negative in the third and fourth quadrants.
the reference angle of 41.8103149 in the third and fourth quadrant is found as follows:
third quadrant = 41.8103149 + 180 = 221.8103149 degrees.
fourth quadrant = 360 - 41.8103149 = 318.1896851 degrees.
your angles that satisfy the equation of 3sin^2(theta) + 2sin(theta) = 0 are:
0,180,360 degrees.
221.8103149, 318.1896851 degrees.
a graph of the equation is shown below:


<img src = "http://theo.x10hosting.com/2021/052201.jpg">