Calculate cos(θ/2) Given sin(θ)=-5/13

[MathRaven]

Homework Statement

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

 

[eumyang]

Homework Statement

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

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.

 

[SammyS]

Homework Statement

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

You need to show some effort before we can help you.

Read the rules for this Forum.