Find cotθ, cscθ, and sinθ, where θ is the angle shown in the figure.

Question

cotθ =

cscθ =

Sinθ =

the hypotenuse side is empty

the other side is 3

the base is 5

the θ is at the bottom between the hypotenuse and base

Give exact values, not decimal approximations. 

Answer 1

the hypotenuse = sqrt(3^2 + 5^2) = sqrt(34)

sin (theta) = other side/hypotenuse = 3/sqrt(34)

cos(theta) = base/hypotenuse = 5/sqrt(34)

csc(theta) = 1/sin(theta) = sqrt(34)/3

cot(theta) = cos(theta)/sin(theta) = 3/5