Trigonometry worksheet asking students to find the exact values of all six trigonometric functions for an angle θ based on given information about its quadrant and one function's value.

A) cos θ = 1/2, sin θ < 0
sin θ = -√3/2, csc θ = -2/√3
cos θ = 1/2, sec θ = 2
tan θ = -√3, cot θ = -1/√3

B) sin θ = -3/4, tan θ > 0
sin θ = -3/4, csc θ = -4/3
cos θ = -√7/4, sec θ = -4/√7
tan θ = 3/√7, cot θ = √7/3

C) sin θ = 1/4, cos θ > 0
sin θ = 1/4, csc θ = 4
cos θ = √15/4, sec θ = 4/√15
tan θ = 1/√15, cot θ = √15

D) sec θ = 3, cos θ < 0
sin θ = -2√2/3, csc θ = -3/(2√2)
cos θ = -1/3, sec θ = -3
tan θ = 2√2, cot θ = 1/(2√2)

E) tan θ = -√5/2, sin θ < 0
sin θ = -√5/3, csc θ = -3/√5
cos θ = 2/3, sec θ = 3/2
tan θ = -√5/2, cot θ = -2/√5

F) cos θ = √3/2, sin θ < 0
sin θ = -1/2, csc θ = -2
cos θ = √3/2, sec θ = 2/√3
tan θ = -1/√3, cot θ = -√3