Question

If sin(a) = -3/5 , where a lies between pi <a < 3pi/2 , then cos (a/2) = ?

Answer 1

sina = -3/5 then cosa = -4/5

if π < a < 3π/2 then π/2 < a/2 < 3π/4

we know that cosa = 2cos^2(a/2) - 1

substituting the value of cosa we have

-4/5 +1 = 2cos^2(a/2) that implies cos^2(a/2) = 1/10

so cos(a/2) = plus or minus(1/√10)

as π/2 < a/2 < 3π/4 and in this interval cos(a/2) is negative

so cos(a/2) = -1/√10