# If Sin(θ)=-5/13

1. Jul 8, 2012

### MathRaven

1. The problem statement, all variables and given/known data

If sin(θ) = -5/13, π < θ < 3π/2, find cos(θ/2)

2. Jul 8, 2012

### eumyang

Given that sin(θ) = y/r, that we're in Quadrant III, and that x2 + y2 = r2, you should be able to find x, and from that, cos(θ).

Then use the cosine half-angle identity
$$\cos \left( \frac{\theta}{2} \right) = \pm \sqrt{\frac{1 + \cos \theta}{2}}$$
to find cos(θ/2). Since π < θ < 3π/2, you know the range of values that θ/2 lie in, so that will tell you whether the square root should be positive or negative.

3. Jul 8, 2012

### SammyS

Staff Emeritus