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:

I Quadrant of cosθ

I Quadrant of Cosθ

I Quadrant of cosθ

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:

II Quadrant of cosθ

II Quadrant of Cosθ

II Quadrant of cosθ

  • 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:

III Quadrant of cosθ

III Quadrant of Cosθ

III Quadrant of cosθ

  • 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:

IV Quadrant of cosθ

IV Quadrant of Cosθ

IV Quadrant of cosθ

  • 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

Graph of cosθ

Graph of Cosθ

Graph of cosθ

Example:

Draw the graph of in the interval to .

Solution:

Graph of cos2θ

Graph of cos2θ

Graph of cos2θ

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