Base concept of Trigonometry and its Derivation

trigonometry_2

Base concept of Trigonometry and its Derivation

Topic discussed in this video:

  • Base Concept of Trigonometry and its derivation

 

One of the beauties of trigonometry is that its rules are equally applicable for all similar triangles because the base concept of trigonometry was derived from the similarity of triangles and in this video, I am going to discuss that base concept with its derivation.

But before I begin our main concept, let’s revise right triangles first.

As we have learned in the right triangles that we have a fixed interior angle of . The side opposite this interior angle is the longest side and it is known as hypotenuse. Because of this fixed interior angle of , the other two interior angles are always complementary. That means,
So, if I assume  as q then  will always be .

As the trigonometry is about the relationships between the interior angles and the side lengths. So, from now onwards, I am going to assume the interior angle q as my main angle for all the concepts and derivations. Also, AB is going to be the opposite side of my main angle and BC is going to be the adjacent side. These special names for all three sides linked with interior angles are going to be very helpful with our main concept and derivation.

Let’s begin the main concept of trigonometry………

Base concept of Trigonometry and its Derivation 1

What is Trigonometry and why we chose right triangles to start learning trigonometry?

trigonometry_1

What is Trigonometry and why we chose right triangles to start learning trigonometry?

Questions discussed in this video:

  • What is Trigonometry?
  • How to start trigonometry?
  • Which triangle is the best option to start trigonometry?
  • Why we choose right triangles for trigonometry?

 

The word trigonometry was derived from two Greek words “trigonon” and “metron”. Trigonon means Triangle and metron means Measure. So, trigonometry is about measurements in a triangle.
Now, what kind of measurements in a triangle?
As you know, a triangle has three sides with three interior angles and we can measure the side lengths and the interior angles of a triangle. And trigonometry is about these measurements. Or to be precise, trigonometry is about relationships between side lengths and the interior angles of triangle.

Now, the question is which type of triangle is the best option to start learning trigonometry?
As you know, we have different types of triangles in maths. On the basis of lengths of sides, we have equilateral triangles in which all three sides are of equal lengths, then we have isosceles triangles in which two sides are of equal lengths and then we have scalene triangles in which all three sides are of different lengths; all three sides are unequal.
On the basis of interior angles, we have right triangles in which one interior angle is of 90 degrees, then we have acute triangles in which all three angles are smaller then 90 degrees and we have obtuse triangles in which one interior angle is greater than 90 degrees. types of triangles

Now, the classification on the basis of interior angles is quite interesting, because we can easily draw a relationship between right triangles, acute triangles and obtuse triangles, which is not quite easily possible in the case of equilateral triangles, isosceles triangles and scalene triangles………