Trigonometric Ratios: Overview, Questions, Preparation

Updated on Jul 23, 2021 04:14 IST

Table of Contents

Trigonometric Ratios
Trigonometric ratios
FAQs

Trigonometric Ratios

Introduced in class 10th, “trigonometric ratios” is a significant chapter for your board exam. This chapter might be introduced in 10th class but you will be studying this topic in the 11th and 12th also. Every student needs to learn the basics well so that they don’t face any challenge afterwards. Trigonometry is basically a branch of mathematics that deals with angles and sides of a right-angled triangle. There are six trigonometric ratios named as sin, cos, tan, cosec, sec, and cot. All these ratios are determined or calculated with the help of the angles and sides of a triangle.

Trigonometric ratios

In a right-angled triangle, the adjacent side is also known as the ‘base’. The side making a right-angle with base is known as perpendicular or the opposite and the slant line is known as hypotenuse. Based on these sided we get the trigonometric ratios as:

Trigonometric Ratios	Formula
Sin θ	P/H
Cos θ	B/H
Tan θ	P/B
Cosec θ	H/P
Sec θ	H/B
Cot θ	B/P

Note: Where θ is a given angle, P is the perpendicular, H being the hypotenuse of a right-angled triangle.

The chapter is taught in 10th standard and it holds a good weightage in the final exams. Trigonometric Ratios is worth approximately 10-12 marks in the board exam. You can expect questions from this chapter -right from one marker to 6 marker questions. You find trigonometry everywhere. So, it is better to learn all the formulas and get a good grip on trigonometry.

Illustrative Examples:

1. A right-angled triangle XYZ has, right-angled at Y, hypotenuse XZ= 8cm, base YZ= 7cm and perpendicular XY= 2cm. If the given ∠XZY = θ, what will be the functions tan θ, sin θ and cos θ.

According to the question, In ∆XYZ,

Hypotenuse, XZ= 8cm

Base, YZ= 7cm

Perpendicular, XY= 2cm

We also know that the trigonometric functions are:

Sin θ = Perpendicular/Hypotenuse =XY/XZ = 2/8

Cos θ = Base/Hypotenuse = YZ/XZ = 7/8

tan θ = Perpendicular/Base = XY/YZ = 2/8

2. What will be the value of tan θ if sin θ = 12/5 and cos θ = 3/5.

It is given that,

sin θ = 12/5 and cos θ = 3/5

We also know that,

Tan θ = Sin θ/Cos θ

Tan θ = (12/5) /(3/5)

Tan θ = 12/3

Tan θ = 4

2. What will be the value of cosec θ, if sin θ= 2/6

We already know that according to the function rule,

Cosec θ= 1/sin θ

Which means;

Cosec θ= 1/ (2/6)

Cosec θ= 6/2

FAQs

Q: Which of the 6 trigonometric ratios are the primary ones?

A: The primary trigonometric ratios from all the 6 of them are sin, cos & tan.

Q: Is there any shortcut to learn all the 6 formulas of trigonometric ratios?

A: There is an easy way to learn all the 6 formulas of trigonometric ratios. Learn the first three (which are also the primary ones) and just reverse them for the next three. E.g.- Reverse of sin will be cosec, then cos will give you sec, and tan will give you cot.

Q: What are the 6 trigonometric ratios that are taught?

A: The six trigonometric ratios are sin, cos, tan, cosec, sec, and tan.

Q: Is there any relationship between functions sin, cos and tan?

A: Yes, the ratio of sin and cos function equals tan. i.e- sinθ/cosθ = Tanθ

Q: Is there any relation between sin, cos, tan & cosec, sec, cot?

A: Cosec, sec & cot are the reverse of sin, cos and tan. i.e- Cosecθ = 1/sinθ Secθ = 1/cosθ Cotθ= 1/tanθ