Question 293867
Without using a caculator, Find cos x/2, given cot x = (-3), pi/2 < x < pi
------------------------
Plot the point (-3,1)
The angle from the Origin is angle x, and is in the 2nd quadrant.
The hypotenuse is sqrt(10), so the cos(x) = -3/sqrt(10) = -3sqrt(10)/10
----------------
Use the half-angle formula:
cos(x/2) = sqrt(2+2cos(x))/2
{{{cos(x/2) = sqrt(2 - 6sqrt(10)/10)/2}}}
{{{cos(x/2) = sqrt((20 - 6sqrt(10))/10)/2}}}
{{{cos(x/2) = sqrt((10 - 3sqrt(10))/5)/2}}}
{{{cos(x/2) = sqrt((50 - 15sqrt(10))/25)/2}}}
{{{cos(x/2) = sqrt((50 - 15sqrt(10)))/10}}}