Question

If sin θ=-36/45 and θ is in quadrant IV then what is sin (θ/2?

Answer 1

To find sin(θ/2) when sin(θ)=-36/45 and θ is in quadrant IV, we use the half-angle formula for sine.

Step-by-step explanation:

To find the value of sin(θ/2) when sin(θ) = -36/45 and θ is in quadrant IV, we need to use the half-angle formula for sine:

sin(θ/2) = √((1 - cos(θ)) / 2)

Since θ is in quadrant IV, the cosine of θ is positive. To find the value of cosine, we can apply the Pythagorean identity: cos(θ) = √(1 - sin^2(θ))

Substituting the given value of sin(θ) into the Pythagorean identity, we find the value of cos(θ) and then substitute it into the half-angle formula to find sin(θ/2).