Trigonometric Functions-I, Objectives, Circular Measure of Angle, Relation Between Degree and Radian

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We have read about trigonometric ratios in our earlier classes.

Image show triangle ABC

Image Show Triangle ABC

Image show triangle ABC

Recall that we defined the ratios of the sides of a right triangle as follows:

And

We also developed relationships between these trigonometric ratios as

, ,

Objectives

Objective

Objective

Objective

Circular Measure of Angle

  • An angle is a union of two rays with the common end point. An angle is formed by the rotation of a ray as well.

  • Negative and positive angles are formed according as the rotation is clockwise or anticlock-wise.

A Unit Circle

  • It can be seen easily that when a line segment makes one complete rotation, its end point describes a circle.

  • In case the length of the rotating line be one unit then the circle described will be a circle of unit radius. Such a circle is termed as .

A Radian

  • A radian is another unit of measurement of an angle other than degree. A radian is the measure of an angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

  • In a unit circle one radian will be the angle subtended at the centre of the circle by an arc of unit length.

A Radian

A Radian

A Radian

Relation between Degree and Radian

  • An arc of unit length subtends an angle of 1 radian. The circumference subtend an angle of radians.

Hence radians , radians , radians

radians radian

or radians radians

Example: Convert

(i) into radians

(ii) radians into degrees.

Solution:

(i) radians

radians or radians

(ii) radians , radians

radians

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