# Trigonometry: Important facts, Techniques and Formulae

Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC syllabus. Today I will tell you the easy method to learn all the basics of trigonometry i.e. Trigonometric Ratios, facts and formulas.

## Trigonometric Ratios

There are six trigonometric ratios. First three are the primary functions and last three are just the reciprocals of above three. Those are written as follows:
• Sin theta
• Cos theta
• Tan theta
• Cot theta
• Sec theta
• Cosec theta
See the following image, You are already well versed with this image. This is a basic right angled triangle.

Points to remember:
1. Usually, student got confused between perpendicular and base. Always remember that out of three sides, perpendicular is that side which is opposite to the given angle.

In following figure, perpendicular (P) is the side which is opposite to the purple shaded angle(given angle)

2. Side opposite to the right angle(shaded red)  is hypotenuse (H).

3. Remaining side is known as base (B).

Now, you must be knowing that all the trigonometric ratios can be derived from these sides. Let us see how.

Sin theta = P/H                       Cosec theta = H/P

Cos theta = B/H                      Sec theta = H/B

Tan theta = P/B                       Cot theta = B/P

Learning all these formulae is somewhat difficult because trigonometry is full of formulas. Let me tell you the very easy method to learn the above formulas.

Following is the basic pattern which you should learn by heart. The easy way to remember this is the way our teachers teach us in schools. I am sure that is the best way to remember this. You can never forget this trick:

(Some People Have) (Curly Brown Hair) (Through Proper Brushing)

Learn the above line and write 3-3 words vertically like:

Some         Curly        Through
People       Brown       Proper
Have           Hair          Brushing

i.e.
S    C    T
P    B    P
H    H    B

 Sin Cos Tan P B P H H B Cosec Sec Cot

Now, It will seem very easy to learn the ratios. Isn't it?

## Basic Formula

Following are some very basic formulae. Go through these formulas once, then we will proceed to the trigonometric ratios of standard angle.

• Cosec theta = 1/ (Sin theta)
• Sec theta = 1/ (Cos theta)
• Cot theta = 1/(tan theta)
• Tan theta = (Sin theta)/(Cos theta)
• Sin^2 theta + Cos^2 theta = 1
• 1+ tan^2 theta = sec^2 theta
• 1+ cot^2 theta = cosec^2 theta

## Trigonometric Ratios of Standard Angles

You must have seen the following table of trigonometric ratios, but so many times you may get confused by remembering the values. Here, I will tell you the basic technique which will help you to learn this table.

 theta 0° 30° 45° 60° 90° Sin theta 0 1/2 1/sqrt2 sqrt3/2 1 Cos theta 1 sqrt3/2 1/sqrt2 1/2 0 Tan theta 0 1/sqrt3 1 sqrt3 Not Defined Cot theta Not Defined sqrt3 1 1/sqrt3 0 Cosec theta 1 2/sqrt3 sqrt2 2 Not Defined Sec theta Not Defined 2 sqrt2 2/sqrt2 1

Firstly, to find the values of Row1
• Write numbers from 0 to 4
• Divide the numbers with 4
• Take the square root of all
0 to 0/4 to 0                                                           0

1 to 1/4 to 1/4                                                        1/2

2 to 2/4 to 1/2     Taking Square root to          1/sqrt2

3 to 3/4 to 3/4                                                         sqrt3/2

4 to 4/4 to 1                                                             1

See. how simple. You just need to divide 4 to numbers 0 to 4, then take square root.

Row2 = It is just the reverse of Sin values. (See table)

Row3 = Value of tan theta is derived by using (Sin theta)/(cos theta)

Row4 = Use Cot theta = 1/ tan theta

Row5 = Use Sec theta = 1/ cos theta

Row6 = Use Cosec theta = 1/sin theta

## Examples with Solution

Example1: Find the value of:

(2tan30^o) / (1+ tan^2 30^o)

Solution: (2tan30^o) / (1+ tan^2 30^o) = (2/sqrt3)/(1+(1/sqrt3)^2)

Solving above will give = sqrt3

Example2: If tan theta= sqrt2/sqrt3, then what will be the value of costheta?

Solution: tan theta = P/B

Therefore, P = sqrt2 and B = sqrt3

using Pythagoras Theorem, H^2 = P^2 + B^2

H^2 = 2+ 3=5
⇒ H = sqrt5

Therefore, Cos theta = B/H = sqrt3/ sqrt5

I hope you understand this topic till now, I will soon update the rest of the topic.
Your valuable feedback will be appreciated.

#### What's trending in BankExamsToday

Smart Prep Kit for Banking Exams by Ramandeep Singh - Download here 