Table of Contents

### What is Trigonometry ?

Trigonometry comes from the Greek words* ** trigonon* (“triangle”) and *metron *(“to measure”). It is a branch of mathematics that deals with the relationship between the sides and angles of a triangle. It is associated with right angled triangles where one angle,as we know, is always 90 degrees. We study it in our Maths classes, wondering where else can it possibly be used?! You would be surprised that it finds its uses in other branches of mathematics, like in complex numbers, infinite series, logarithms and calculus. Its principles are used in various other fields as well.

While studying trigonometry, it is to be kept in mind that :

- Sides and angles that touch are called
**adjacent**and thus every side has two adjacent angles. - Sides and angles that don’t touch are called the
**opposite**. - In a right angle triangle, the side opposite the right angle is called the
**hypotenuse**and the two remaining sides are called**legs**. - If two angles or two sides are given, they can be worked with to measure the rest of the details.

### Why study trigonometry?

Of course, mastering trigonometry opens the door for a teaching profession and research work that requires its knowledge. But remember how it got mentioned above, about the other fields that this concept influences today? Well …..

Trigonometric functions calculator is used to alter wave patterns in sounds in the music industry. Music producers and sound engineers employ it to create music which appeals to the listeners. Who would have thought!

Also architects utilise trigonometry in erecting buildings and to create the illusions of curved surfaces on structures. It finds its use in making buildings earthquake resistant by improving the structure and its elements.

Movies have shown the use of trigonometry in launching rockets and placing satellites in their required positions in space. It is without a doubt true that trigonometry is used to calculate their speeds which have to be accurate to avoid any unfortunate events.

And not to forget, the video game industry runs due to trigonometry. Wondering how? Well it is used to set up the obstacles and other structures that pop up on your screen and also to calculate the path of anything thrown or launched in a game by a player from any point in the game. Guess nerds do rule everywhere!!

### What is a Trigonometric Table?

To determine angles and distances, a trigonometry table has been developed. The main functions in trigonometry are Sine, Cosine and Tangent. A Trigonometric table helps to find the values of angles such as 0°, 30°, 45°, 60° and 90°. It consists of trigonometric ratios – sine (sin) , cosine(cos), tangent(tan), cosecant(cosec), secant(sec), cotangent(cot).

**How To Remember the Trigonometry Table?**

The Trigonometry ratios table is dependent upon the trigonometry formulas.

Below are the few steps to memorize the trigonometry table.

Before beginning, try to remember below trigonometry formulas.

- sin x = cos (90° – x) : reciprocal of cosecant = opposite / hypotenuse
- cos x = sin (90° – x) :reciprocal of secant = adjacent / hypotenuse
- tan x = cot (90° – x): reciprocal of cotangent = opposite / adjacent
- cot x = tan (90° – x) : reciprocal of tangent = adjacent /opposite
- sec x = cosec (90° – x): reciprocal of cosine = hypotenuse / adjacent
- cosec x = sec (90° – x): (reciprocal of sine) = hypotenuse / opposite
- 1/sin x = cosec x
- 1/cos x = sec x
- 1/tan x = cot x

**Steps to Create a Trigonometry Table****:**

**Step 1: Make the table**

Create a table with the top row listing the angles such as 0°, 30°, 45°, 60°, 90°, and write all trigonometric functions in the first column such as sin, cos, tan, cosec, sec, cot.

**Step 2: Determine the value of sin.**

**Step 3: Determine the value of cos.**

**Step 4: Determine the value of tan.**

**Step 5: Determine the value of cot.**

The value of cot is equal to the reciprocal of tan. The value of cot at 0° will obtain by dividing 1 by the value of tan at 0°. So the value will be:

cot 0° = 1/0 = Infinite or Not Defined

Same way, the table for a cot is given below.

**Step 6: Determine the value of cosec.**

**Step 7: Determine the value of sec.**

We must appreciate how Trigonometry influences us and helps in our everyday lives. If you find it intriguing and want to master it, then register free for a demo class with **Edulyte. **

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