Given cotx = −3 and secx > 0, find cos x/2.

Question

Given cotx = −3 and secx > 0, find cos x/2.

Options>

a. 3 sqrt(2)/4

b. sqrt(2)/4

c. 3

d. 2 sqrt (2)

Answer 1

cotx = - 3 and secx > 0, then x in Quadrant IV. Then tanx = - 1/3, secx = sqrt(1 + 1/9) = sqrt(10)/3.

So cosx = 3/sqrt(10). Now 270° < x < 360°, then 135° < x/2 < 180ˆ and cos(x/2) is negative.

Because cos(x/2) = - sqrt((1 + cosx)/2) = - sqrt((1 + 3/sqrt(10))/2) ≈ - .9871

There is now right answer to choose. Cos(x/2) must be negative