# Secant Graph

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As secant is a reciprocal of cosine function so for some values this function is discontinuous.

We know that sec x ≤ -1 or sec ≥ 1.

First, we graph y = cos x and then y = sec x immediately below it. Compare the y-values in each of the 2 graphs and assure yourself they are the reciprocal of each other.

**Phase shift in secant-graph**

The secant function is y= sec(bx -c) - d

Period = 2π/b and phase shift = c/b

vertical shift = -d

**Example 1 :**y = sec(πx -1)

b = π

period =2π/b = 2π/π = 2

phase shift=c/b=1/π= 1/3.14 = 0.3184 So the graph will shift to right side by 0.3184 units.

If we draw a secant curve with no shifts then the (x,y)coordinates are (0,1),(1,-1) and (2,1)

After shifting the coordinates will be (0 +0.3184,1),(1.3184,-1) and (2.3184,1)

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**Example 2 :**y = – sec(x + π/2) + 3

**Solution :**

Guide function: y = – cos(x + π/2) + 3 a = –1 ; b = 1 ; c = – π/2 and d = 3

period = 2π/1 = 2π

phase shift = x + π/2 = 0

⇒ x = -π/2

vertical shift =3

Now you can easily graph this.

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**Practice**

1) y = -5 sec(πx/4 - π/2)-3

2) y = 2 sec(x)

3) y = sec(x - π)

4) y = -sec(x) + 1

5) What is the period of y = −4sec(πx)?

6) Find the period and phase shift of y = -4sec(πx/4 + π/4)

7) Find the period and phase shift of y = -4sec(πx/8 + π/4)

8) What is the period of y = 2sec(x/8)?

9) Find the period and phase shift of y = sec(3x) + 4

10) What is the period of y = sec(-2x)?

**secant graph**

Graph Dictionary

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