How do I solve for cos (x/2)?

Question

cot x = -3, and "x" is in Quadrant 2. How do I solve for cos (x/2)?

Answer 1

me hate trig me sick of trig me take trig 4 2 long(6mts in the last 2 school yrs)

ok if cot x=-3 then tan x=-1/3
then x=inversetan -1/3
then cos(inversetan(-1/3)/2)
type that in ur caculator
x = .987
then x is about .987

BUT since its in quaderant 2 (remember astc?) its negative

so x = -.987

Answer 2

cot x = -3 therefore tan x = -1 / 3

To find out what "x" is you first must find the reference angle.

reference angle = inverse tan (1 / 3)
= 18.43 degrees

Since the reference angle is in the second quadrant, I can subtract 18.43 deg. from 180 deg. to get "x"

x =180 - 18.43
= 161.6 deg

Now I can plug "x" into Cos (x/2)

Cos (161.6/2)
= Cos(80.8)

It's positive so it must be in either the first or fourth quadrants.

The reference angle is 80.8 deg so therefore:

Angle 1 = 80.8 deg
Angle 2 = 360 - 80.8 = 279.2 deg

Answer 3

x = 106.621 degrees
x/2 = 53.31 degrees
cos(x/2) = .597479