What is the Usefulness of Trig Identities?

Industry Outlook Team | Wednesday, 20 April 2022

In the subject of mathematics, where is the real use of the trig identities? These are required while solving a trigonometric equation or expression. When we do the trigonometrical operations, these trigvalues hold true on both sides of the equation.
When we do geometrical mathematics, the trig functions like the sine, cosine, and tangent are all involved together which is the value of one or more angles.
Did you know about the trig functions? In geometry, we studied the sine, cosine, tangent, cotangent, secant, and cosecant. These all are related to trigonometry, and they form the trigonometric functions.

Can you Name the List of the Trigonometric Identities?

In the study of trigonometry, there are various identities or representations of trigonometry. These identities are required in solving the many trigonometrical problems at hand. With the use of these trigonometrical formulae and identities, we can solve many difficult equations in a quick way.
1. The reciprocal trigonometric identities:
The reciprocal trigonometric identities are as under:
● Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
● Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
● Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

2. Pythagorean Trigonometric Identities:
Three Pythagorean trigonometric identities take the form of the right-angle triangle theorem or the Pythagoras theorem. They are as follows:
● sin2 a + cos2 a = 1
● 1+tan2 a = sec2 a
● cosec 2a = 1 + cot2 a

3. Ratio Trigonometric Identities
The trigonometric ratio identities are these identities given below:
● Tan θ = Sin θ/Cos θ
● Cot θ = Cos θ/Sin θ

Define Area of Parallelogram

Before understanding what is the area of a parallelogram, do you know what a parallelogram looks like?
A parallelogram can be a similar structure to a quadrilateral which has two of its sides equal to each other. Solely, the parallelogram is a two-dimensional figure consisting of four sides.

What Do We Mean By the Area of the Parallelogram?

The area of the parallelogram is nothing but the region which is enclosed by the outer line that is the four sides of the parallelogram.
The area of the parallelogram can be estimated as the product of the length and height of the figure.

How Will You Calculate the Area of Parallelogram?

The area of the parallelogram can be also calculated if you know the base and the height of the parallelogram. The area of the parallelogram can be calculated in yet another way - The area of the parallelogram can be calculated with the help of the intersecting angles, also you can calculate if you know the length of the parallel sides with the angles which lie between the sides. Thus, in total there are three methods of deriving the area of the parallelogram, they are:
● When we have the data of the base and height of the parallelogram.
● When we do not know the measurement of height.
● When the data of the diagonals are given.

This study was devoted to trig identities and area of parallelogram. Both the studies were based on geometrical mathematics. Students have higher chances to score good marks in the geometrical part of mathematics if practiced and understood properly.

In the trig identities, we learned that there is a connection with the trigonometric equations. The trig identities are very much involved in these equations. We have also learned about the three trig identities which help in making difficult problems easier.

In the area of a parallelogram, we studied what a parallelogram looked like and we also took note of the formula of the area of the parallelogram. We knew different possibilities of finding the area of the parallelogram.

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