Tuesday, 20 June 2017

Trigonometry I – What is Trigonometry with Trigonometric Ratios for SSC and Other Exams

Trigonometry may appear to be complex but is simple if approached the right way. Read on to understand what is trigonometry along with an explanation of trigonometric ratios.

trigonometric ratios
What is Trigonometry? Trigonometry is a branch of mathematics that deals with the length of the side of a triangle and the angles in a triangle. Trigonometry is not a very common topic in competitive exams, however it is asked in a few exams like SSC CGL and SSC CHSL where it is given good weightage. Therefore it makes it essential for us to study this topic. Trigonometric ratios are one of the fundamental pillars of trigonometry. We will start our series on trigonometry by discussing the different trigonometric ratios.


What is Trigonometry- Different Systems for Measuring an Angle    

There are 3 different ways to measure an angle.   
1.   Sexagesimal or English System: Degrees       
In this system the angle is measured in terms of degrees. As per this system, one right angle constitutes 90°, one degree constitutes 60’ and one minute is 60’’.
trigonometric ratios   
2.   Centesimal or French System: Grades       
In this system the angle is measure in terms of grade. The root word of this system is ‘cent’ which means 100, so in this system one right angle is equal to 100g (g here stands for grades), one grade is equal to 100’ and each minute is equal to 100’’.
trigonometric ratios
3.   Circular System: Radians      
In this system the angle is measure in terms of radians. One radian (1c) is the angle subtended at the centre of a circle by an arc of length equal to the radius of the circle.
trigonometric ratios
On comparing the three systems we can say-
trigonometric ratios  
The above relationship can be used to convert an angle in one system to an angle in the other system.
1c = 1 x 180/p = (180 x 7)/22 = 570 17’ 45’’
So remember-
trigonometric ratios

What is Trigonometry- Relationship between Radius, of the Length Arc and the Angle Subtended at the Centre

Before we move ahead to trigonometric ratios, let us discuss the relationship between the radius, length of the arc and angle subtended at the centre, in a circle.
Look at the diagram below, where we consider a circle with radius ‘r’, centre ‘O’ and an arc of length ‘l’.
trigonometric ratios
The length of the arc is the product of the radius and the angle subtended at the centre. (The angle is in terms if radians)-
trigonometric ratios
trigonometric ratios
trigonometric ratios

Trigonometric Ratios

Trigonometric ratios are the simply the ratios of different sides of a right angled triangle with respect to acute angle. So for trigonometric ratios we simply take two sides and get their ratios, and based on the different pair of sides we choose, we get different trigonometric ratios.
trigonometric ratios
Here we have a right angled triangle, which had a 900 angle at the vertex A. We know the side opposite to the right angle is called the Hypotenuse, the initial line is the Base of the triangle and the third side is the perpendicular. We also have an angle θ at the vertex B. With respect to this angle we are going to consider the various trigonometric ratios.


The side opposite to θ is the perpendicular and the side adjacent to θ is the base. 
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
trigonometric ratios
Stay tuned for more on trigonometry and till then don't stop practicing!
trigonometric ratios
trigonometric ratios
Whatsapp Share Share on whatsapp

0 comments:

Post a Comment