Table of contents  
Introduction to Trigonometry  
Measurement of Angles  
Tratios (or Trigonometric Functions)  
New Definition of Tratios 
There are two systems of measurement of angles:
(i) Sexagesimal or English System: Here 1 right angle = 90 (degrees)
1 = 60’ (minutes)
1’ = 60" (seconds)
(ii) Circular System: Here an angle is measured in radians. One radian corresponds to the angle subtended by an arc of length ’r ’ at the centre of the circle of radius r. It is a constant quantity and does not depend upon the circle's radius.
(a) Relation between the two systems: Degree = Radian*180 / π
(b) If θ is the angle subtended at the centre of a circle of radius 'r',
by an arc of length 'l' then l / r = θ
Representation of Angle in Circular System
Note: l, r are in the same units and θ is always in radians.
Example.1. If the arcs of the same length in two circles subtend angles of 60° and 75° at their centres. Find the ratio of their radii.
Sol: Let r_{1} and r_{2} be the radii of the given circles and let their arcs of the same length s subtend angles of 60 and 75 at their centres.
Now,
⇒ 4r_{1} = 5r_{2} ⇒ r_{1} : r_{2} = 5 : 4
A Right Angled Triangle
In a rightangle triangle:
sin θ = p / h
cos θ = b / h
tan θ = p / b
cosec θ = h / p
sec θ = h / b
cot θ = b / p
'p' is perpendicular, 'b' is base and 'h' is hypotenuse.
Note : The quantity by which the cosine falls short of unity i.e. 1  cos θ, is called the versed sine θ of θ and also by which the sine falls short of unity i.e. 1 sinθ is called the coversed sine of θ.
The three main trigonometric functions are then defined in terms of r and the coordinates x and y:
(The other functions are reciprocals of these)
This can give negative values of the trigonometric functions.
335 videos845 docs218 tests

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1. Can you explain the concept of angles in trigonometry? 
2. What are Tratios (Trigonometric Functions) in trigonometry? 
3. How are Tratios defined in trigonometry? 
4. What is the new definition of Tratios in trigonometry? 
5. How can I apply the concept of angles and Tratios in JEE exams? 
335 videos845 docs218 tests

Logarithm: Concepts with Examples Doc  6 pages 
Log Functions Video  20:04 min 
Finding Maxima and Minima using Derivatives Doc  2 pages 

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