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

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

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:

is positive as is positive.

and when we approach from the right.

As varies from to , increases from to .

II Quadrant:

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:

is negative as is negative.

and when the angle approaches in the counter clockwise direction.

As varies from to , increases from to .

IV Quadrant:

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 :