Question

If sin(θ) = -5/13, and θ is in Quadrant IV, then what is tan(θ/2)?

A. 5/12
B. -12/5
C. -5/12
D. 12/5

Answer 1

To find the value of tan(θ/2), we can use the half-angle identity for tangent. Given sin(θ) = -5/13 and θ in Quadrant IV, we can determine cos(θ). Substituting values into the half-angle identity, we find tan(θ/2) = 5/12.

Step-by-step explanation:

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

tan(θ/2) = sin(θ) / (1 + cos(θ))

Given that sin(θ) = -5/13 and θ is in Quadrant IV, we can determine cos(θ) using the Pythagorean identity:

cos(θ) = sqrt(1 - sin^2(θ))

In Quadrant IV, both sin(θ) and cos(θ) are negative. Plugging in the given values, we find:

cos(θ) = sqrt(1 - (-5/13)^2) = -12/13

Now, substituting sin(θ) = -5/13 and cos(θ) = -12/13 into the half-angle identity, we have:

tan(θ/2) = (-5/13) / (1 + (-12/13)) = 5/12