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.

_______________________________________________________________________

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

Period = 2π/b and phase shift = c/b

vertical shift = -d

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)

_______________________________________________________________

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.

______________________________________________________________________

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)?

Graph Dictionary

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers