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

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

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

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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