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You might have come across various trigonometric formulas and trigonometric identities while solving sums of trigonometry and you face difficulty in remembering those formulas and identities. If this is true, you need not worry. We are here to help you with some of the most efficient ways to remember those formulas and identities so that you can excel in the chapter of trigonometry. But before learning those tricks, it is important for us to brush up the concepts of trigonometry and know about various trigonometric formulas and trigonometric identities. While learning about trigonometric formulas, we consider them for right-angled triangles only. The different problems of trigonometric ratios, product identities, and Pythagorean identities can be solved using trigonometric formulas.
What are Trigonometric Ratios?
The ratios of different sides of a right-angled triangle are known as trigonometric ratios. Since trigonometry is the branch of mathematics that deals with sides and angles of a right-angled triangle, trigonometric ratios are evaluated on the basis of sides and angles. We all know that the three sides of the triangle are known as hypotenuse (the longest side), perpendicular (opposite side to the angle) and the base (adjacent side to the angle).
Let us learn about the different trigonometric ratios. We have six different trigonometric ratios; they are as follows:
- Sine: The ratio of the perpendicular side of a right-angled triangle to that of the hypotenuse is known as sine.
- Cosine: The ratio of base of a right-angled triangle to that of the hypotenuse is known as cosine.
- Tangent: The ratio of the perpendicular side of a right-angled triangle to that of the base is known as tangent.
- Cosecant: It is the multiplicative inverse of sine.
- Secant: It is the multiplicative inverse of cosine.
- Cotangent: It is the multiplicative inverse of tangent.
Different Sets of Trigonometric Formulas
- sin.sinX + cos.cosX = 1
- 1 + tan.tanX = sec.secX
- 1 + cot.cotX = cosec.cosecX
- sin (90°-x) = cos x
- cos (90°-x) = sin x
- tan (90°-x) = cot x
- cot (90°-x) = tan x
- sec (90°-x) = cosec x
- cosec (90°-x) = sec x
- sin (2x) = 2 sin(x) cos(x)
- cos (2x) = cos.cos(x) – sin.sin(x)
- tan (2x) = [2tan(x)]/ [1−tan2(x)]
- sin 3x = 3sinx – 4sin.sin.sinx
- cos 3x = 4cos.cos.cosx – 3cosx
- tan 3x = (3tanx – tan.tan. tan x)/ (1-3tan.tanx)
- sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
- cos(x+y) = cos(x)cos(y) – sin(x)sin(y)
- tan(x+y) = tan x + tan y/ (1-tan x. tan y)
- sin(x-y) =sin(x)cos(y)-cos(x)sin(y)
- cos(x-y) =cos(x)cos(y)+sin(x)sin(y)
Tips and Tricks to Learn Trigonometric Ratios and Trigonometric Formulas Easily
There are various mnemonics that help in memorizing trigonometric ratios. We will discuss about few of them below:
1. Pandit Badri Prasad Har Har Bole
Where P from Pandit is for Perpendicular and H from Har is for Hypotenuse, resulting in sin θ = Perpendicular/Hypotenuse.
B from Badri is for Base and H from the Har (middle word) is for Hypotenuse, resulting in cos θ = Base/Hypotenuse.
P from Prasad is for Perpendicular and B from Bole is for Base, resulting in tan θ = Perpendicular/Base. Interesting, is it not? Let us learn one more.
2. Some People Have Curly Brown Hair Turned Permanently Black
Some People Have: Sin θ = Perpendicular/Hypotenuse
Curly Brown Hair: Cos θ = Base/Hypotenuse
Turned Permanently Black: Tan θ = Perpendicular/Base
You can remember basic trigonometric formulas and then you can use those formulas to derive other formulae. This technique increases your recalling power and helps you to analyse different formulas which is very important to solve questions of trigonometry.
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