Question

Please help me too in if sin w=-0.5 and w is a degree measure in the third quadrant, find w.

Answer 1

Do you remember your unit circle? If sin ω = was -1/2, then it would be 7π/6. If you're unfamiliar with the unit circle, we can derive it.

So, you know that sin is OPPOSITE/HYPOTENUSE, and it's in the third quadrant, where x and y would be negative. If sin ω = -1/2, that means that ω = 1/sin*(-1/2), or sin^(-1)*(-1/2). Let's ignore the negative for now and plug sin^(-1)*(-1/2) into your calculator in radians. You get (1/6)π. But that's in Quadrant 1. We want it in Quadrant 3.

In one complete revolution, or 360°, there are 2π radians. That means, if you want to rotate it 180°, you need to add π to what you originally got.
π+(1/6)π=(7/6)π.

I highly recommend you memorize the unit circle if you haven't already, because you'll need it from Precalculus on.