If 4sintheta = -3, solve for theta given 0°>_theta>_360°

Answer:311.41 degreesStep-by-step explanation:If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).Let's assume we're in Quadrant IV.  Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.According to the Pythagorean Theorem,  (-3)^2 + x^2 = 4^2, or,x^2 = 16 - 9 = 7.Then x is either √7 or -√7.To find the angle Ф, use the inverse sine function:Ф = arcsin (-3/4).  Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees.  We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."