Given sin x = -3/5 and x is in quadrant 3. What is the value of tan x/2

Solution:

It is given that

sin x = -3/5 where x is in the quadrant 3

We have to find the value of tan x/2

The relation of tan x/2 with sine and cosine is

\(\\tan(x/2)=\pm \sqrt{\frac{1-cos (x)}{1+cos(x)}} \\ \\=\frac{1-cos(x)}{sin(x)} \\ \\=\frac{sin(x)}{1+cos(x)}\)

From the triangle, we observe that cosine = -4/5

This is a notable triangle of side length 3, 4 and 5

So we get,

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

tan (x/2) = -3

Therefore, the value of tan x/2 is - 3.

Given sin x = -3/5 and x is in quadrant 3. What is the value of tan x/2

Summary:

Given sin x = -3/5 and x is in quadrant 3. The value of tan x/2 is - 3.