if sec(theta) =-6 and tan (theta) < 0 what is the othe four trig functions

Question

find the other four trig functions

Answer 1

Given Sec(theta) = -6 and tan(theta) < 0

Sec(theta) and tan(theta) are negitive in second quadrant.

Sec(theta) = hypotenuse/adjacent side

Hypotenuse = 6 and adjacent side = 1

From the pythageron therom opposite side is = √35

Sin(theta) = opposite side/hypotenuse = √35/6

Cos(theta) = adjacent side/hypotenuse = -1/6

Cot(theta) = adjacent side/opposite side = -1/√35

Csc(theta) = hypotenuse/opposite side = 6/√35