NCERT Class 11-Math's: Chapter –3 Trigonometric Functions Part 1
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3.1.1 Overview
The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘matron’ which means measuring the sides of a triangle. An angle is the amount of rotation of a revolving line with respect to a fixed line. If the rotation is in clockwise direction the angle is negative and it is positive if the rotation is in the anti-clockwise direction. Usually we follow two types of conventions for measuring angles, i.e., (i) Sexagesimal system (ii) Circular system.
In sexagesimal system, the unit of measurement is degree. If the rotation from the initial to terminal side is of a revolution, the angle is said to have a measure of
. The classifications in this system are as follows:
In circular system of measurement, the unit of measurement is radian. One radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius of the circle. The length s of an arc of a circle of radius r is given by , where θ is the angle subtended by the arc at the centre of the circle measured in terms of radians.
3.1.2 Relation between degree and radian
The circumference of a circle always bears a constant ratio to its diameter. This constant ratio is a number denoted by π which is taken approximately as for all practical purpose. The relationship between degree and radian measurements is as follows:
3.1.3 Trigonometric Functions
Trigonometric ratios are defined for acute angles as the ratio of the sides of a right angled triangle. The extension of trigonometric ratios to any angle in terms of radian measure (real numbers) are called trigonometric functions. The signs of trigonometric functions in different quadrants have been given in the following table:
3.1.4 Domain and range of trigonometric functions
Functions | Domain | Range |
3.1.5 Sine, cosine and tangent of some angles less than 90°
Not defined |
3.1.6 Allied or Related Angles
The angles are called allied or related angles and are called conterminal angles. For general reduction, we have the following rules. The value of any trigonometric function for is numerically equal to
(a) the value of the same function if n is an even integer with algebraic sign of the function as per the quadrant in which angles lie.
(b) corresponding cofunction of θ if n is an odd integer with algebraic sign of the function for the quadrant in which it lies. Here sine and cosine; tan and cot; sec and cosec are cofunctions of each other.
3.1.7 Functions of negative angles
Let be any angle. Then