Suppose cosalpha35 and alpha is sin quadrant III Find the fo

Suppose cos(alpha)=-3/5 and alpha is sin quadrant III. Find the following

A) Sin (alpha/2)

B)cos(alpha/2)

Solution

cos(alpha)=-3/5 and alpha is sin quadrant III

Use the half angle formula : sin(x/2) = sqrt[(1 -cosx)/2]

A) sin(alpha/2) = sqrt[(1 + 3/5)/2]

= sqrt(8/10)

= 2/sqrt5

B) cos(x/2) = sqrt[ (1 - sin^2(x/2)]

= sqrt[ 1 - 4/5]

= 1/sqrt5