Trigonometric Ratios of Compound Angles

About Trigonometric Ratios of Compound Angles

Trigonometry is one of the most important topics in maths and physics. Trigonometry is the division of maths, which is essentially about angles and measurement. The functions that come under trigonometry are made up of compound angles, multiple angles, and trigonometric ratios. These functions are implemented for finding accurate results. Here we will discuss trigonometric ratios of the compound angles along with some of the questions and their answers.

An angle can be defined as the ray that has its rotation around the startup point. The point where rotation starts is initial and the point where it tends to stop is the final one. When the ray is rotated in the anticlockwise direction, it will create a positive angle. However, rotation of the ray in clockwise direction will have a negative angle. The angle can be measured either in the degrees or radians.

What are Compound Angles?

The compound angle can be defined as an algebraic sum of two or more than two angles. The compound angles represent various trigonometric identities. Here is the complete list of the trigonometric ratios for compound angles.

1) cos A cos B – sin A cos B = cos (A + B)

2) cos A cos B + sin A cos B equals to cos (A – B)

3) sin A cos B + cos A sin B equals to sin (A + B)

4) sin A cos B – cos A sin B = sin (A – B)

5) Sin2 A - Sin2 B= sin (A + B) sin (A – B) = cos2B - cos2 A

6) cos2 A – Sin2 A - Sin2 B = cos (A + B) cos (A – B) = cos2B - Sin2 A

7)  tanA + tanB / 1 - tanAtanB = tan (A+B

8) tanA - tanB / 1 + tanAtanB = tan (A - B)

Similarly you can find for the difference or sum of the sines and cosines, multiples, for the sub-multiple and multiple angles, trigonometric  ratios of the multiples of an angle by referring to the Vedantu notes on “Trigonometric ratios of compound angles”. You can also refer to several problems with solutions that use compound angle formulae. 

Vedantu is one of the leading online learning platforms that provides a host of high quality learning resources and material to the students. The web content and the app provided by Vedantu covers a host of different subjects, topics, and academic related content for the students to refer and benefit from it. Vedantu also incorporates videos and innovative teaching material for helping the students with the complex concepts and thus preparing them for clearing their exams. 

FAQs on Trigonometric Ratios of Compound Angles

1. What is trigonometry and what are its applications?

Trigonometry is essentially the division of geometry, which is widely used in measuring the sides of the triangle. It is very easy to solve the problems with the help of trigonometric concepts along with the measurement of the triangles. Trigonometry has several applications and it is widely used amongst scientists, navigators, engineers, and meteorologists since it serves various purposes that assists these professionals and provides effective solutions to some of the issues that are encountered. 

2. What is meant by the zero angle?

Zero angle is an angle that has a degree of zero. The visualisation process of the zero angles is often found to be difficult and tough. For instance, the two lines that create the angle which is greater than the zero degrees. If both lines pass through one another without any inclination then there is a possibility of the zero angles. This explains the concept of the zero angle in trigonometry. 

3. What are the basic ratios in trigonometry?

The names of the three basic ratios in trigonometry are known as “Sine”, “Cosine”, and “Tangent”. In the right angled triangle, we are able to find out sine, or the cosine, or the tangent, for both non - 90 degree angles. If the ABC is considered as the right angled triangle then we are able to write the expression for the angle A with the help of sine, cosine, and the tangent. 

4. What is the meaning of a double angle?

The double angle is essentially a concept where it is related to three of the common trigonometric ratios, which includes sine (sin), cosine (cos), and tangent (tan).  The sole and the very purpose of these ratios is basically expressing the connection that exists between sides of the right angled triangle for certain or specific angles within that triangle. Double angle involves increasing the size of angle to make it twice of its size. 

5. How can I refer to “Trigonometric ratios of compound angles” notes from Vedantu?

Vedantu is one of the most prominent learning platforms with a wide range of learning resources made available to the students. If you want to refer to the Vedantu notes on “Trigonometric ratios of compound angles” then it can be downloaded for free in the form of a PDF file. The notes are available to download from the website as well as the app.