# Trigonometric Functions-I, Graph of Cos θ as θ Varies from 0 to 2π

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## Graph of Cos Θ as Θ Varies from 0 to 2π

As in the case of , we shall also discuss the changes in the values of when assumes values in the intervals , and

I Quadrant:

In the interval , point lies in the first quadrant.

Therefore, is positive but decreases from to as increases from to .

Thus in this interval decreases from to .

is positive.

II Quadrant:

In the interval , point lies in the second quadrant.

Therefore point lies on the negative side of x-axis. So in this case is negative and decreases from to as increases from to .

Thus in this interval decreases from to .

is negative.

III Quadrant:

In the interval , point lies in the third quadrant.

Therefore, remains negative as it is on the negative side of x-axis.

Therefore is negative but increases from to as increases from to .

Hence in this interval increases from to .

is negative.

IV Quadrant:

In the interval , point lies in the fourth quadrant.

Therefore point lies on the positive side of x-axis.

Therefore is positive and increases from to as increases from to .

Thus in this interval increases from to .

is positive.

## Graph of Cos Θ

Example:

Draw the graph of in the interval to .

Solution: