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

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Graph of Csc Θ as Θ Varies from 0 to 2π

cscθ as θ Varies From 0 to 2π

Cscθ as Θ Varies from 0 to 2π

cscθ 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:

I Quadrant of cscθ

I Quadrant of Cscθ

I Quadrant of cscθ

  • is positive as is positive.

  • when is very small, is also small and therefore, the value of is very large.

  • As varies from to , decreases from to .

II Quadrant:

II Quadrant of cscθ

II Quadrant of Cscθ

II Quadrant of cscθ

  • is positive as is positive.

  • and when the revolving line approach in the counter clockwise direction.

  • As varies from to , increases from to .

III Quadrant:

III Quadrant of cscθ

III Quadrant of Cscθ

III Quadrant of cscθ

  • is negative as is negative.

  • When is slightly greater than , is very large and negative and also .

  • As varies from to , changes from to .

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

IV Quadrant:

IV Quadrant of cscθ

IV Quadrant of Cscθ

IV Quadrant of cscθ

  • is negative as is negative.

  • Therefore, as approaches .

  • As varies from to , changes from to .

Graph of :

Graph of cscθ:

Graph of Cscθ:

Graph of cscθ:

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