Trigonometry

Revision Notes
Class 11 Maths
Chapter 3 – Trigonometric Functions


TRIGONOMETRIC RATIOS & IDENTITIES

1. The meaning of Trigonometry

Tri Gon Metron

  

3 sides Measure

As a result, this area of mathematics was established in the ancient past to measure
a triangle's three sides, three angles, and six components. Time-trigonometric
functions are utilised in a variety of ways nowadays. The sine and cosine of an
angle in a right-angled triangle are the two fundamental functions, and there are
four more derivative functions.



2. Basic Trigonometric Identities
(a) sin 2   cos2   1: 1 sin  1; 1 cos  1  R

(b) sec2   tan 2   1:| sec | 1  R

(c) cosec2   cot 2   1:| cosec | 1  R



Trigonometric Ratios of Standard Angles


Angles(In 0 30 45 60 90 180 270 360
Degrees)




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, Angles(In 0      3 2
radians) 6 4 3 2 2



Sin 0 1 1 3 1 0 -1 0
2 2 2



Cos 1 3 1 1 0 -1 0 1
2 2 2



Tan 0 1 1 3 Not 0 Not 1
3 Defined Defined


Cot Not 3 1 1 0 Not 0 Not
Defined 3 Defined Defined


Csc Not 2 2 2 1 Not -1 Not
Defined 3 Defined Defined


Sec 1 2 2 2 Not -1 Not 1
3 Defined Defined



The relation between these trigonometric identities with the sides of the triangles
can be given as follows:

 Sine (theta) = Opposite/Hypotenuse

 Cos (theta) = Adjacent/Hypotenuse
 Tan (theta) = Opposite/Adjacent



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