A function value and a quadrant are given Find the other fiv

A function value and a quadrant are given. Find the other five function values. Give exact answers. cot theta = - 5. Quadrant IV (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.) (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.)

Solution

cot theta=-5 /1

therefore adjacent=5 and opposite= -1

therefore hypotenuse= sqrt(5^2 +(-1)^2)=sqrt 26

sin theta=opposite/hypotenuse= -1/sqrt26=-sqrt26/26

cos theta= adjacent/hypotenuse=5/sqrt26=5sqrt26/26

tan theta= 1/cot theta=-1/5

sec theta=1/cos theta= sqrt26/5

csc theta=1/sin theta= -sqrt 26