Question

Solve the equation sin(2x-\[Pi])=-(1/2)
how would i go about solving this?

Answer 1

1. Let theta=2x-pi.
2. Find arcsin(0.5) - this should be 30 degrees (or pi/6 rads).
3. As the sin of theta is <0, it lies in the 3rd & 4th quads, where the angles will be (3n-2) pi + (pi/6) rads or else, (2n)pi - (pi/6) rads (where n ∈ Z+).
4. For case #1 [when theta=(3n-2)pi+(pi/6) rads], find x (x = theta+pi/2).
5. For case #2 [when theta=(2n)pi-(pi/6) rads], find x.