Graphing Secant Functions

Graphing Secant Functions

How to graph secant functions: graph, example, and its solution.

Graph

y = sec x = 1/cos x

Secant is the reciprocal of cosine:
y = sec x = 1/cos x.

See the graphs of
y = cos x (gray) and
y = sec x (white, blue).

If y = cos x = ±1,
y = sec x touches y = cos x.
(y = sec x = 1/[±1] = ±1)

If y = cos x = 0,
then those x values
are the vertical asymptotes of y = sec x.
(y = sec x = 1/[±0] = ±∞)

So, to graph the secant function,
first draw the cosine function,
then draw the secant function.

Graphing cosine functions

The blue part is one cycle of y = sec x.

So the period of y = sec x is 2π:
same as y = cos x.

The asymptotes are x = + π/2:
when cos x = 0.

Example

Sketch the given function's graph. y = sec 2x (0 <= x <= 2pi)

Roughly draw one cycle of y = cos 2x
with its amplitude and period.

Amplitude: 1
Period: 2π / |2| = π

Graphing cosine functions

Use these values to draw y = cos 2x. (gray)

Then draw y = sec 2x
by using the cosine graph.

If y = cos 2x = ±1,
y = sec 2x touches y = cos 2x.

If y = cos 2x = 0,
then those x values
are the vertical asymptotes of y = sec 2x.