Use your graphing calculator to find all radian solutions in the interval 0 ≤ x < 2π ; round your answers to four decimal places sin2x=3/7

Question

Any help with this would be great. The solutions must also be in radians. Thank you!!!

Answer 1

Sine is positive in quadrants I and II, that is between 0 and π. arcsin(3/7)=0.4429+2πn and 2.6987+2πn approximately, where n is an integer. Therefore 2x=0.4429+2πn and 2.6987+2πn, making x=0.2215+πn and 1.3493+πn. We choose n so that we get values of x between 0 and 2π, so x must not exceed 6.2832.

n=0: x=0.2215, 1.3493;

n=1: x=3.3630, 4.4909.

The solution is shown graphically below as the intersections of the red curve with the blue line, and the green shows the upper limit for x.