find cos y and tan y if csc y = -√6/2 and cot y > 0

Question

 Use the Pythagorean identities to find each function value.

Answer 1

sin y = 1/csc y = -2/sqrt(6)

basic identity: sin^2y + cos^2y = 1

so 2/3 + cos^2y = 1

and cos^2y = 1/3

cos = -sqrt(3)/3 (since cot y > 0, sin y and cos y must have same sign)

tan y = sin y /cos y = -2/sqrt(6) / -sqrt(3)/3 = -6/sqrt(18) = -2/sqrt(2)