An Introduction to Trigonometry

Basic Definition – Trigonometry is a branch of mathematics which deals with the relationship between the sides and the angles of right-angled triangles. Here the term ‘Right-angled’ triangle is very important.

Let’s understand this with an example.

Consider a girl looking at the top of a tower which is few distances apart from her legs. Now, this will form a right-angled triangle whose height can be calculated without actually measuring it physically.

In this chapter, we will be learning about some standard trigonometric identities by using the relation between angles and the sides of the right-angled triangle.

### # Trigonometric Ratios-

• Consider a right triangle with sides AB, BC and AC with C as a right angle.
• Now, considering an acute angle let’s say Angle A, then side opposite to A i.e. a is called the hypotenuse. Also, side b is called the adjacent side.

The trigonometric ratios are defined as:

These ratios are generally represented in their short forms. These are sin A, cos A, tan A, cosec A, sec A and cot A respectively.

Notes:

1. cosec A, sec A and cot A are the inverse of sin A, cos A and tan A respectively.
2. sin A /cos A = tan A and therefore cos A/sin A = cot A

Example 1: Given sinA =4/5, Find all other trigonometric ratios of angle A.

Solution: Let’s draw a right triangle ∆ABC right angled at B.

Now, Given that sin A =4/5

∴BC/AC =4/5
∴ BC = 4k and AC= 5K, where K is a constant.

Now, In ∆ABC, applying Pythagoras Theorem,

(AC)2 = (AB)2 + (BC)2

∴ (5K)2 = (AB)2 + (4K)2

∴ AB = 3K

Similarly, cosec A = 1/ sin A = 5/4
And, sec A = 1/ cos A = 5/3
And, cot A = 1/ tan A = 4/3 Answer

## Trick To Remember All the Trigonometric Ratios

We will remember all the ratios using a mnemonics as

Here Look at the ratios and the words

• For Sin theta, we have Pandita/Hara which is P/H
• Similarly For Cos theta we have Badri/hara which is B/H
• Similarly for Tan theta, we have Prasad/Bola which P/B
• For other ratio take the reciprocal of the angles.
• Such as for Cosec theta it is H/P
• Sec Theta it is H/B and for Cot theta, it is B/P.

This note is Contributed by
Vishesh Meena
3rd Year, Electrical Engineering,
IIEST
[email protected]