Question

If sin(θ) = -3/5 and θ is in quadrant III, find tan(θ/2).

Answer 1

The value of tan(θ/2) when sin(θ) = -3/5 and θ is in quadrant III is -3.

Step-by-step explanation:

To find the value of tan(θ/2), we need to use the half-angle identity for tangent.

The half-angle identity for tangent is given by:

tan(θ/2) = sin(θ) / (1 + cos(θ))

Since we are given that sin(θ) = -3/5, we can substitute this value into the formula:

tan(θ/2) = (-3/5) / (1 + cos(θ))

Since cos(θ) is negative in quadrant III, we take the negative square root:

cos(θ) = -4/5

Now we can substitute the values of sin(θ) and cos(θ) into the half-angle identity for tangent:

tan(θ/2) = (-3/5) / [1 + (-4/5)]

Simplifying the expression:

tan(θ/2) = (-3/5) / (1/5) = -3