# Multiple Angle Formulas

## Multiple Angle Formulas

Multiple Angle Formulas is a very important Mathematical concept. It is part of Trigonometry. The area of mathematics known as trigonometry is concerned with the mathematical properties of specific angles and how to employ those properties in computations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions are depicted in the figure in relation to a right triangle. The sine of the angle, or sin A, for example, is the ratio between the side opposite to an angle and the side opposite to the right angle (the hypotenuse); other trigonometric functions are defined similarly. Before computers rendered trigonometry tables obsolete, these functions—which are characteristics of the angle, regardless of the size of the triangle—were listed for numerous angles. In geometric figures, unknown angles and distances are derived from known or measured angles using trigonometric functions.

The need to calculate angles and distances in disciplines like astronomy, map making, surveying, and artillery range finding led to the development of trigonometry. Plane trigonometry deals with issues involving angles and lengths in a single plane. Spherical trigonometry takes into account applications to similar issues in more than one plane of three-dimensional space.

Applications: Trigonometrical applications can be found in many areas of daily life. Astronomy is one of the well-known fields where trigonometry is used to calculate the distances between the Earth and other planets and stars. It is used to create maps for navigation and geography. Finding an island’s location in relation to its longitude and latitude uses applications of trigonometry as well. Even today, some of the most cutting-edge techniques employed in engineering and the physical sciences are founded on trigonometric ideas.

Trigonometry is used in a variety of fields, including surveying, astronomy, and building. The two most prevalent subjects are astronomy and physics, in which it is used to measure the separation between planets and stars, determine their velocity, and analyse waves. Among the applications are: Oceanography, seismology, meteorology, physical sciences, astronomy, acoustics, navigation, electronics, and a host of other disciplines. It is also useful to calculate the length of long rivers, gauge a mountain’s height, etc.

Astronomers have utilised spherical trigonometry to determine the positions of the sun, moon, and stars.  Trigonometry is also employed in the following areas:

Trigonometry is necessary for criminology or crime scenes to ascertain the approximate cause of a collision in a car accident or at what angle a gunshot was fired. Trigonometry is used by marine scientists to determine the depth of sunlight that influences algae’s capacity for photosynthesis. Waves of sound and light can be described using trigonometric functions.

Oceanographic wave and tidal height calculations are made using trigonometry.

Algebra and trigonometry are the foundations of calculus.

## Multiple Angle Formulas

Trigonometric functions frequently contain Multiple Angle Formulas. Although it is impossible to directly obtain the values of Multiple Angle Formulas, their values can be calculated by expanding each trigonometric function. Multiple Angle Formulas is another name for the multiple-angle trigonometric function. The many angle formulas employ the double and triple angles formulas. The common functions used for the Multiple Angle Formulas include sine, tangent, and cosine.

Trigonometric functions frequently contain Multiple Angle Formulas. Although it is impossible to directly obtain the values of Multiple Angle Formulas, their values can be calculated by expanding each trigonometric function.

## Multiple Angle Formulae

When the term “Multiple Angle Formulas” is used to describe trigonometric functions with multiple angles. Multiple Angle Formulas include double, triple, and half-angle formulas.

Trigonometric functions’ half-angles make up half-angle equations.

Formulas for double angles are composed of trigonometric functions’ double angles.

Trigonometric functions’ triple angles make up triple-angle equations.

### List of Multiple Angle Formulae

• Half Angle Formula
• Double Angle Formula
• Triple Angle Formula

It is common for trigonometric functions to contain Multiple Angle Formulas. Despite the fact that it is impossible to directly obtain their values, their values can be calculated by expanding each trigonometric function. Mathematical concepts like this are very important. Essentially, it’s a part of trigonometry. Known as trigonometry, this field of Mathematics focuses on the properties of angles and how to use them.  One can study the Multiple Angle Formulas on the Extramarks website or mobile application. One is required to register on the website of Extramarks in order to be able to access the learning resources provided on the concerned website.

### Generalized Multiple Angle Formulae

Students can learn more about Generalised Multiple Angle Formulas from the various resources provided by Extramarks. Extramarks provides resources in accordance with the latest NCERT syllabus. All the resources provided are prepared after consideration of past years’ question papers. Further, the resources are written in an easy-to-understand language. Students can rely on the resources provided by Extramarks as they are written by expert subject teachers and are proofread regularly.

### Sample Problems on Multiple Angle Formulas

To understand any topic better, students should solve practice problems on it. To understand the topic of Multiple Angle Formulas well, students can solve questions based on it. The practice questions will help students to apply their knowledge. If they face any difficulty in solving questions of Multiple Angle Formulas, they can refer to the resources offered by Extramarks. Extramarks provided resources are of high quality. The resources such as revision notes help students strengthen their basics.