What is Cot(cos^-1(-39/89))?

1 Answer
Oct 11, 2015

#cot(cos^-1(-39/89)) = -39/80#

Explanation:

Let #theta = cos^(-1)(-39/89)#

Then #cos(theta) = -39/89#

and #theta# is in Q2, so #sin(theta) >= 0# and

#sin(theta) = sqrt(1-cos^2(theta)) = sqrt(1-39^2/89^2) = sqrt((89^2-39^2)/89^2) = sqrt((7921-1521)/89^2) = sqrt(6400/89^2) = sqrt(80^2/89^2) = 80/89#

So:

#cot(theta) = cos(theta)/sin(theta) = (-39/89)/(80/89) = -39/80#