Question

If cos(x) = -3/5, and c lies in the third quadrant, find tan(x/2)

Answer 1

Explanation:

Since cos(x) = -3/5, we can use the Pythagorean identity to find sin(x):

sin(x) = sqrt(1 - cos^2(x)) = sqrt(1 - (-3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5

Since c lies in the third quadrant, both cos(x) and sin(x) are negative. Therefore, we have:

cos(x) = -3/5 and sin(x) = -4/5

Now, we can use the half-angle formula for tangent:

tan(x/2) = sin(x)/(1 + cos(x)) = (-4/5)/(1 + (-3/5)) = (-4/5)/(2/5) = -2

Therefore, tan(x/2) = -2.