CBSE Class 11 Mathematics Trigonometric Function Notes

 XI: Maths

Chapter-3: Trigonometric Function

Chapter Notes

Top Concepts

1. An angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex.

2. If the direction of the rotation is anticlockwise, the angle is said to be positive and if the direction of the rotation is clockwise, then the angle is negative.

3. If a rotation from the initial side to terminal side is (1/360)^th of a revolution, the angle is said to have a measure of one degree, I t is denoted by 1^o.

4. A degree is divided into 60 minutes, and a minute is divided into 60 seconds. One sixtieth of a degree is called a minute, written as 1’, and one sixtieth of a minute is called a second, written as 1”

Thus 1^o =60',1'=60

8 .Cosine is even and sine is odd function
cos(-x) = cos x
sin(-x) = - sin x

9. Signs of Trigonometric functions in various quadrants

In quadrant I, all the trigonometric functions are positive.

In quadrant II, only sine is positive. In quadrant III, only tan is positive,

quadrant IV, only cosine function is positive. This is depicted as follows

10. In quadrants where Y-axis is positive (i.e. I and II), sine is positive and in quadrants where X-axis is positive (i.e. I and IV), cosine is positive

11. A function f is said to be a periodic function if there exists a real number T>0, such that f(x + T) = f(x) for all x. This T is the period of function.

12. sin (2π+ x ) = sin x so the period of sine is 2π. Period of its reciprocal is also 2π

13. cos (2π+ x) = cos x so the period of cos is 2π. Period of its reciprocal is also 2π

14. tan (π+ x) = tan x Period of tangent and cotangent function is π

15.The graph of cos x can be obtained by shifting the sin function by the factor 2π

16. The tan function differs from the previous two functions in two ways (i)tan is not defined at the odd multiples of π/2 (ii) tan function is not bounded.

17. Function Period
y=sin x            2π

y=sin (ax)       2π/a

y=cos x           2π

y=cos (ax)      2π/a

y=cos 3x        2π/3

y=sin 5x        2π/5

18. For a function of the form
y= kf(ax+b) range will be k times the range of function x, where k is any real number if f(x)= sine or cosine function range will be equal to R-[-k, k] if function is of the form sec x or cosec x, Period is equal to the period of function f by a. The position of the graph is b units to the right/left of y=f(x) depending on whether b>0 or b<0

19. The solutions of a trigonometric equation for which 0 ≤ x ≤ 2π are called principal solutions.

20.The expression involving integer ‘n’ which gives all solutions of a trigonometric equation is called the general solution.

21. The numerical smallest value of the angle (in degree or radian) satisfying a given trigonometric equation is called the Principal Value. If there are two values, one positive and the other negative, which are numerically equal,
then the positive value is taken as the Principal value.
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