Cosine Rule
What is the Meaning of Cos?
Cos is a primary function related to the sums of Trigonometry and calculus. It is simply the cosine of a specific angle of a triangle. The cos of different angles has their specific values which play a vital role in the case of solving trigonometric problems. In calculus, it relates to the Sin function and together they make formulas and identities. There are many concepts of trigonometry (conceptual geometry) and you need to learn them thoroughly to get good marks in the examination.
Cosine: Definition
As per basic trigonometry is concerned, it deals with various operations with the right-angled triangle. Different denotations are made according to the relations of each line segment of the triangle and its relation with the other. These line segments have specific names such as the Opposite (Height of the triangle), Adjacent (base of the triangle), and Hypotenuse (the line joining the tip of the base to height).
The relations of the line segments of the triangle are expressed with three specific functions known as Sine, Cosine, and Tangent. In the case of the sums, these terms are abbreviated as sin, cos, and tan.
Here, you will get to know about Cosine. If you consider a right-angled triangle, the angle made by the base and hypotenuse will be considered as θ. In the case of the Cosine function, the angle between the adjective and hypotenuse is only taken into account.
So, cos θ = Base / hypotenuse
The Cos Formula
The details of the Cos formula is mentioned below:
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In reference to the above picture you can say that in the Triangle ABC, Cos Alpha can be written as:
Cos α = The dividend of the side AC and AB that is AB/AC
So, Cos α = b/h (Which matches the concept totally)
Tables and Identities of Cosine
As a student learning trigonometry, you must keep the tables related to the Cosine function in mind.
Generally, the values of different angles are given in the table. For the basic level trigonometry, you will only need to know the values till 90 degrees starting from 0 degrees. You can refer to the trigonometry study materials from Vedantu to know all the values. Learning these values will help you to understand what is the meaning of cos.
If you take mathematics in higher studies, you might have to learn the values of Cosine angles up to 360 degrees.
Apart from the values of different angles, you need to learn the different identities of Cosines. As the identities of Cosine can help you to solve problems easily. As Cosine is a primary function it is mainly related to Sine (sin). All the identities of Cosine are actually formulas of Cosine that can help you to jump steps accordingly. All you need to do is memorize the identities thoroughly.
Law of Cosine
The Law of Cosine is the better way to know about Cosine. The relationship between the sides of the right-angled triangle is mathematically displayed here the law is given below:
c2 = a2 + b2 + 2ab cos α
In the above formula, variables a, b, and c denote the three sides of the triangle. To know more about the derivation of the Cosine formula you need to visit the Vedantu site.
Why is the Concept of Cosine so Vital?
The concept of Cosine is vital because it is one of the primary trigonometric functions that you need to know. Without knowing all about Sine, Cosine, and Tangent, neither you can acquire any knowledge about the inverses of the basic functions nor you can solve the advanced trigonometric problems.
Moreover, it is vital because the concepts related to trigonometry has a close relationship with calculus. Poor knowledge about trigonometry can restrict you to study higher mathematics in higher standards. The concepts of Cosine will be applicable in mathematical streams like differential calculus, integral calculus, and differential equations.
Solved Examples
Q1. What is the value of Cos θ in a right-angled triangle whose sides are 12cm and 20 cm respectively?
Ans. To find the value of cos θ in the triangle you need to apply the Pythagoras Theorem.
As per the Pythagoras theorem PR= sq. root [(12)2 + (20)2] = sq, root (544) cm.
12 / sq. root (544)
= 0.514
Q2. What are the laws of Cosines?
Ans: The laws of Cosines in terms of advanced trigonometry are dependent on the square root of the sides. You can find it on the Vedantu site.
FAQs on Cosine Meaning
Q1. What is the Right Way to Practise Trigonometry Problems?
Answer: As the problems of Trigonometry are vast, you need to clear the concepts first. Give full dedication to learning the formulas before you actually move on to solving the problems. The best you do is to start solving the primary sums repeatedly as a startup. Later, you can move on to solving the advanced sums. Make sure you have chosen the right book from where you solve the sums. Otherwise, you might not get common questions in the examination. The best you can do is go through the solved examples in your book first and determine the concept you need to use while solving the problem.
Q2. How to Learn the Values and Laws of Cosine?
Answer: As a student learning secondary level mathematics pin school, you need to understand the fact that you must always avoid memorizing anything related to trigonometry. It can be dangerous because a slight change-up in the numbers can make your sums go wrong. The best you can do is to learn the concepts at first. The values of Cosines should always be learned on the basis of a right-angled triangle. You can visit the Vedantu site and refer to the study materials that can give you the knowledge as per the requirement. Moreover, the guidance of experienced teachers can help you to learn the laws of Cosine depending on the theory rather than just memorizing it.