Ratios

sine x = (side opposite x)/hypotenuse

cosine x = (side adjacent x)/hypotenuse

tangent x = (side opposite x)/(side adjacent x)

In the figure below, sin A = a/c, cosine A = b/c, and tangent A = a/b.

Reciprocal Ratios

cotangent x = 1/tan x = (adjacent side)/(opposite side) 

secant x = 1/cos x = (hypotenuse)/(adjacent side) 

cosecant x = 1/sin x = (hypotenuse)/(opposite side)

Cofunctions

sin x = cos (90o - x) 

tan x = cot (90o - x) 

sec x = csc (90o - x) 

cos x = sin (90o - x) 

cot x = tan (90o - x) 

csc x = sec (90o - x) 

Example:

1. Problem: Find the function value of

cot 60o.

Solution: Use the cotangent's cofunction

identity to rewrite the problem.

tan (90o - 60o)

tan 30o

The tangent of 30o is

(SQRT(3))/3