a radian measure in terms of degree measure and a degree measure in terms of radian measure. Using approximate value of π as , we have radian = π ° = ° ′ approximately. Also ° = π radian = .01746 radian approximately. The relation between degree measures and radian measure of some common angles are given in the following table: A O P − − Q Fig .
Degree ° ° ° ° ° ° ° Radian π π π π π π π TRIGONOMETRIC FUNCTIONS Notational Convention Since angles are measured either in degrees or in radians, we adopt the convention that whenever we write angle θ° , we mean the angle whose degree measure is θ and whenever we write angle β , we mean the angle whose radian measure is β . Note that when an angle is expressed in radians, the word ‘radian’ is frequently omitted. Thus, π π and ° ° are written with the understanding that π and π are radian measures. Thus, we can say that Radian measure = π × Degree measure Degree measure = π × Radian measure Example Convert ° ′ into radian measure.
Solution We know that ° = π radian. Hence ° ′ = degree = π × radian = π radian. Therefore ° ′ = π radian. Example Convert radians into degree measure.
Solution We know that π radian = °. Hence radians = π × degree = × degree = degree = ° + × minute [as ° = ′ ] = ° + ′ + minute [as ′ = ″ ] = ° + ′ + . ″ = ° ′ ″ approximately. Hence radians = ° ′ ″ approximately.
Example Find the radius of the circle in