Trigonometric Functions-I, to Find the Variations and Draw the Graph of Sec θ as θ Varies from 0 to 2π

Doorsteptutor material for SAT Mathematics is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 169K)

To Find the Variations and Draw the Graph of Sec Θ as Θ Varies from 0 to 2π

X'OX and Y'OY be the axes of coordinates

X'OX and Y'OY be the Axes of Coordinates

X'OX and Y'OY be the axes of coordinates

  • Let and be the axes of coordinates. With centre , draw a circle of unit radius.

  • Let be any point on the circle. Join and draw .

  • Variations will depend upon .

I Quadrant:

I Quadrant of secθ

I Quadrant of Secθ

I Quadrant of secθ

  • is positive as is positive.

  • and when we approach from the right.

  • As varies from to , increases from to .

II Quadrant:

II Quadrant of secθ

II Quadrant of Secθ

II Quadrant of secθ

  • is negative as is negative.

  • when we approach from the left. Also .

  • As varies from to , increases from to .

  • It is observed that as passes through , changes from to .

III Quadrant:

III Quadrant of secθ

III Quadrant of Secθ

III Quadrant of secθ

  • is negative as is negative.

  • and when the angle approaches in the counter clockwise direction.

  • As varies from to , increases from to .

IV Quadrant:

IV Quadrant of secθ

IV Quadrant of Secθ

IV Quadrant of secθ

  • is positive as is positive.

  • When is slightly greater than , is positive and very large.

  • Also . Hence decreases from to as varies from to .

  • It may be observed that as passes through , changes from to .

Graph of :

Graph

Graph

Graph

Developed by: