Reallife Application of Inverse Function Sadman Arefin Introduction

Real-life Application of Inverse Function Sadman Arefin

Introduction to Inverse Trigonometric Function Inverse trigonometric function is a significant concept of mathematics. It is also used in important fields like aviation, engineering, and in important scientific calculations. Inverse trigonometric functions are basically used to measure angles. These functions are the inverse of the basic trigonometric functions. These are represented as sin^-1(x), cos^-1(x), tan^-1(x).

Application: The horizontal distance between the base of a building and the observer is 50 ft. The height of that building is 43 ft. What is the angle of elevation? ? ?

Theory: In this application, we have to find the angle of elevation. Angle of elevation is a key mathematical concept. Angle of elevation is the angle between the horizontal and the line from the object to the observer. First, I set up a right triangle and I used inverse trigonometric function ratios in order to solve for the missing angle. I choose the application because it is a great way to reveal the use of trigonometric functions in our daily lives. If we want to find the height of an object, or the distance between two things, or the angle of something, we can always use the trigonometric function ratios. In order to find the appropriate angle of elevation, using the trigonometric function ratios in the right way is very important.

Procedure For Solving the Problem: Given: 1. Horizontal distance = 50 ft 2. Height of the building = 43 ft So, here we have to find the angle of elevation, which is labeled by “theta”. So we set up a right triangle and label the above information. Since, we are trying to figure out the angle labeled by theta, the opposite side to this angle is measured 43 ft and the adjacent side is measured 50 ft. Since we have the measure of the opposite side and the adjacent side to the angle of this right triangle, we can set up a inverse tangent function to configure the angle of elevation. Tan^-1 (opposite side/adjacent side) = theta.

Learning From the Application: - 1. I learned how to set up a right triangle and use inverse trigonometric function ratios to find the missing angle. 2. Next point I learnt from doing this application is that trigonometric functions can be used in our everyday life. For example: to configure height or distance. 3. Now, I got a clear idea about the major difference between the basic trigonometric functions and its inverses. We can use the basic trigonometric function to solve for the missing sides of a right triangle and the inverse trigonometric functions to find the angles of a right triangle.