5.2 Graphs of Reciprocal Trigonometric Function

The graphs of y = cscx, y = sec x, and y = cot x are periodic. They are related to the graphs of the primary trigonometric functions as reciprocal graphs.

Graph of Cosecant

Cosecant

The Cosecant of an angleis the ratio of length of the hypotenuse and the opposite side.

csc (q) = hypotenuse / Opposite

The cosecant is the inverse of the sine and is given by the relation

csc q = 1 / sin q

• Graph of cosecant function:

y = f (x) = csc (x)

Secant Graph.

Secant of an angleis the ratio of length of the hypotenuse and the opposite side.

Sec (q) = hypotenuse / opposite

The secant is the inverse of the sine and is given by the relation
sec q = 1 / cos q

• Co-function for secant

Relations between the secant and cosine functions are the co-function of the other.
Sec A = cos (90° - x)

y = f (x) = sec x

Graph of Cotangent .

Below see cotangent function based on right angle triangle -

• An angleis the ratio of length of the adjacent side and the length of the opposite side is known as Cotangent.

Cot (q) = adjacent / opposite

• It is the inverse of the tangent and its relation is given as

Cot (q ) = 1 / tan q

• It is the ratio of cosine and sine functioncan be defined as

Cot (q) = cos q / sin q

Graph for Cotangent function:
y = f (x) = cot x