trigonometry hw help

Question

Given secθ= √17/4 and tanθ<0

find the exact value of the other five trigonometric function values using square roots and fractions as necessary.

Answer 1

It's quadrant IV

cos(theta) = 1/sec(theta) = 4/sqr17

sin(theta) = -1/sqr17

csc(theta) = -sqr17

tan(theta) = -1/4

cot(theta) =-4

It's a 1-4-sqr17 right triangle

y^2=17-4^2 = 1 (one side squared = hypotenuse squared minus the other side squared)

y=-1

sin(theta) = y/sqr17

csc(theta) =sqr17/y

tan(theta) =y/4

etc.