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 Maths, like in complex numbers, infinite series, logarithms and calculus. We use principles of trigonometry in various other fields.
Trigonometry Ratios-Sine, Cosine, Tangent
Sine, Cosine and Tangent are the three main trigonometry functions or ratios. We know them better as sin, cos and tan.
Now, let us take a right-angled triangle to understand these functions better. The longest side is the hypotenuse, and the sides opposite to it are the adjacent and opposite sides.
While studying trigonometry, keep 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-angled 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.
Unit Circle
The unit circle is one of the more valuable tools to come out of a trig class. The unit circle is a great way to calculate the angles of cos, sin and tan directly since the radius is 1. Consider theta to be an angle.
The length of the hypotenuse is equal to the radius of the unit circle, which is 1. Therefore, we can write the trigonometry ratios as:
Sin θ y/1 = y
Cos θ x/1 = x
Tan θ y/x
What is a Trigonometric Table Values?
To determine angles and distances, a trigonometry value chart has been developed. The main functions in trigonometry are Sine, Cosine and Tangent. A Trigonometric values 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 = reciprocal of cosecant = opposite / hypotenuse
- cos x =reciprocal of secant = adjacent / hypotenuse
- tan x = reciprocal of cotangent = opposite / adjacent
- cot x = reciprocal of tangent = adjacent /opposite
- sec x = reciprocal of cosine = hypotenuse / adjacent
- cosec x = (reciprocal of sine) = hypotenuse / opposite
Steps to Create a Trigonometry Table Chart:
- 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.
Important Trigonometric Angles
These are angles are those through which different trigonometric functions can be represented.
Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Trigonometry angles can be expressed in terms of trigonometric ratios as:
- θ = sin-1 (Perpendicular/Hypotenuse)
- θ = cos-1 (Base/Hypotenuse)
- θ = tan-1 (Perpendicular/Base)
Trigonometry and Calculus
Students who take up calculus in high school require a strong base in trigonometry. It is because the trigonometric functions are often used in questions. For example, in Calculus, the trigonometric functions are used to analyse rotating bodies.
Also, in a calculus course, almost everything is done in radians. The following table gives some basic angles in both degrees and radians.
| Degree | 0 | 30 | 45 | 60 | 90 | 180 | 270 | 360 |
| Radians | 0 | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
You can refer to the following for additional reading:
For effective strategies that will make you into a Maths ninja, read our blog
Trigonometry and its applications
Of course, mastering trigonometry opens the door for a teaching profession and research work that requires its knowledge. But remember how it mentioned above, about the other fields that this concept influences today? Well …..
Trigonometric functions calculator is used to altering wave patterns in music industry sounds. Music producers and sound engineers employ it to create music that appeals to the listeners. Who would have thought!
Also, architects utilise trigonometry in erecting buildings to create the illusions of curved surfaces on structures. It finds its use in earthquake-resistant buildings by improving the structure and elements.
Movies have shown trigonometry in launching rockets and placing satellites in their required positions in space. It is undoubtedly true that trigonometry is used to calculate their speeds, which must be accurate to avoid unfortunate events.
And not to forget, the video game industry runs due to trigonometry. Wondering how? It is used to set up obstacles, other structures that pop up on your screen and calculate the path of anything thrown or launched in a game by a player from any point in the game. So guess nerds do rule everywhere!!
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Frequently Asked Questions
As we know it today, Trigonometry was crafted by the Greek astronomer Hipparchus. He was the first to construct a table of values for a trigonometric function.
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. It is associated with right-angled triangles where one angle, as we know, is always 90 degrees.engage visitors instantly.
There are six trigonometric ratios.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Definitely! Trigonometry is an essential part of Mathematics. It deals with the relationship between the sides and angles of triangles. You can quickly get a grip over it if you approach it the right way. If you face any difficulty in handling it, feel free to contact us
There are three primary functions of trigonometry: Sine function, Cosine function, and Tangent functions.
The most commonly used acronym to remember these ratios is SOHCAHTOA, which stands for “Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent.”
Trigonometry is no longer confined to classroom use. You will be amazed to know that:
Architects utilise trigonometry in erecting buildings to create the illusions of curved surfaces on structures.
Music producers and sound engineers employ it to create music that appeals to the listeners.
It is used to set up obstacles, other structures that pop up on your screen and calculate the path of anything thrown or launched in a video game.
Yes. A solid foundation in trigonometry helps me understand and do calculations in Calculus class. It is because the trigonometric functions are often used in questions. For example, in Calculus, the trigonometric functions are used to analyse rotating bodies.
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