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

Because of the signs of cos and cot, the angle is in quadrant 3 where cos is negative and tan is positive.

(You might want to remember the mnemonic "AllSIgnTanCos" for the functions which are positive in each quadrant.)

The magnitude of the tan is (1/2) sqrt(2) and the magnitude of the cos (1/3)sqrt6).