# Jadhav Angular Formula

**Jadhav Angular Formula** evaluates the **angle between any two sides** of any triangle given length of all the sides, invented by Indian mathematical scholar **Jyotiraditya Jadhav.**

## Contents

## Introduction

In any triangle given sides a,b and c , with **longest side c** the **angle between the sides a and b** can be found by:

#### Nomenclature:

**Cosine function :**The cosine function is one of the basic functions encountered in trigonometry (the others being the cosecant , cotangent, secant, sine , and tangent ). Let be an angle measured counterclockwise from the x -axis along the arc of the unit circle . Then is the horizontal coordinate of the arc endpoint.- : square of length of one side among the angle
- : square of length of other side among the angle

- : square of length of the longest side/ opposite side to the angle

## Visual use

Let the **angle angle between side length a and b be Q**

Now as per the equation angle Q will be:

## Applications

**Astrophysics:**For finding angles between the vector of celestial bodies.

**Aerodynamics:**In finding the glide angle, angle of climb and various angles of attack.

**Navigation:**In finding real time locations.

**Geography:**In calculating distances between geographical locations.**Geometry**: In finding angles between the two sides of any triangle.

**Robotics:**In operating arms and for studying robotic movements through vectors.**Teleportation and Quantum Physics:**In studying oscillating motions of particles.

## Trigonometric Cosine function

Now as in the figure of "Trigonometric Circle" as the angle theta increases and the transition line **goes beyond 1st quadrant**, the value of some trigonometric functions change from positive to negative, like **cosine function the ratio will be negative in the second and 3rd quadrant,** the angle is **always calculated from positive x-axis.** So in-case cosine function inverse of the is a negative value then the angle which gives exactly same ratio in positive will be considered and subtracted from 180 or radians (while dealing with radians) to get exact angle from x-axis.

The generalized formula where the ratio would be (-x), then exact angle can be found like this:

(while using degrees)

(while using radians)

## Other inventions by Jyotiraditya Jadhav

Read more about Jyotiraditya Jadhav **here.**