Exponential Functions vs Trigonometric

A mathematical function that is used in various real-life or real-world situations is known as an exponential function. The exponential functions are generally used in finding the exponential growth and decay of the exponential or in computing and determining model populations and calculating investment.

On the other hand, trigonometry is the branch of mathematics that deals with the relationship of shapes and the length of triangles.

There are three basic trigonometric ratios: sine, cos, and tan. This article will tell you about exponential functions, exponential formulas, and exponential graph representation. 

Introduction to the exponential function

In context mathematics, the functions are defined in the form of f(x) = ax , where “x” is the variable and where “a” is known as the base of the exponential function or also called as constant. An exponential function formula can be described as f(x) = ax, where the input is defined as the x and the exponent. The curve of the exponent depends upon the exponential function, and so it depends on the value of x. The most ordinarily used exponential function base is a transcendental number denoted by (e), with an approximate value of about 2.71828 and up to 23 decimal places.

The Formula for Exponential Function

The formula of exponential formula function is widely used in mathematics and is a very important mathematics formula. It can be represented as 

f(x) = ax

Where a>0 and values of a are not equal to 1.

X is any real number.

If in a condition, the value of the given variable is negative, then the range of the function is (range of x)  -1 < x < 1

 Where “a” is the constable, and x is the variable.

Introduction to a Trigonometric Function

The trigonometric functions are also known as the circular functions, or they can be easily defined as the functions defined for the angles of a triangle. The trigonometric functions give the relationship between the sides of the triangle and the angles of the triangle. There are basic trigonometric functions such as sine, cosine, cos, tan, cot, cosec. There are numerous trigonometric formulae and trigonometric identities that establish the relationship between the trigonometric functions or circular functions and also help in determining the angle of the triangle.

Identities of Trigonometric Functions

• Odd and even functions

The sec and cos function is considered as even function, while all the other functions come under the category of odd functions;

sin(-x) = -sin x

tan(-x) = -tan x

cos(-x) = cosx

cot(-x) = -cot x

cosec(-x) = -cosec x

sec(-x) = sec x

• Periodic functions

• Difference and sum identities

• Pythagorean Identities

Derivative of Exponential Function

The derivative of a function ex with respect x is ex or can be written mathematically as;

d(ex)/dx = ex,

 here the function f(x) = ex has a very special property, which means that the derivative of this function is the function itself only. It can be represented as 

f’(x) = ex = f(x)

Conclusion

Exponential functions are utilised to solve real-world problems. The functions of exponentials are used for determining the growth of the exponential functions and the decay in the exponential functions. The most common base used in the exponential functions is the transcendental number (e), which has an approximate value of up to 23 decimal places.

The exponential function can be represented as f(x) = ax , where a >0 and the value of a is not equal to 1, and x is any real number. The exponential growth can be represented as y=a(1+r)^x, whereas on the other hand, the exponential decay can be represented as 

y = a(1-r)^r.