Question

Given tanx=8/15 when pi < x < 3pi/2, find tan x/2.

Answer 1

`tan(x/2)=-4`

Explanation:

we know that

The angle x belong to the III quadrant -----> given problem

step 1

Find the angle x

`x=arctan(8/15)=28.07\°`

Remember that the angle x belong to the III Quadrant

so

`x=28.07\°+180\°=208.07\°`

step 2

Find angle x/2

`x/2=208.07\°/2=104.035\°`

step 3

Find tan(x/2)

`tan(104.035\°)=-4`