Trigonometric, hyperbolic functions with invers and Sum function

1. Trigonometric, hyperbolic functions with invers
and Sum function
Prepared By:
Sozan Hasan
Sahar Abas
Gashben Sabah
Chewar Muhammed
Supervised By:
M. Media

2. Trigonometry, the branch of mathematics concerned with specific functions of angles and their application
to calculations. There are six functions of an angle commonly used in trigonometry. Their names and
abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The six trigonometric functions
Trigonometry developed from a need to compute angles and distances in such fields
as astronomy, mapmaking, surveying, and artillery range finding.
Trigonometry

3. The hyperbolic function
The hyperbolic functions are analogs of the circular function or the trigonometric functions. The hyperbolic function occurs in the
solutions of linear differential equations, calculation of distance and angles in the hyperbolic geometry, Laplace’s equations in the
cartesian coordinates. Generally, the hyperbolic function takes place in the real argument called the hyperbolic angle. The basic
hyperbolic functions are:
• Hyperbolic sine (sinh)
• Hyperbolic cosine (cosh)
• Hyperbolic tangent (tanh)
From these three basic functions, the other functions such as hyperbolic cosecant (cosech), hyperbolic secant(sech) and hyperbolic
cotangent (coth) functions are derived.

4. Hyperbolic Sine Function
The hyperbolic sine function is a
function f: R → R is defined by f(x) =
[ex– e-x]/2 and it is denoted by sinh
x
Sinh x = [ex– e-x]/2
Graph : y = Sinh x
Hyperbolic Cosine Function
The hyperbolic cosine function is a
function f: R → R is defined by f(x) =
[ex +e-x]/2 and it is denoted by cosh x
cosh x = [ex + e-x]/2
Graph : y = cosh x
The hyperbolic cosine function is a function f:
R → R is defined by f(x) = [ex +e-x]/2 and it is
denoted by cosh x
cosh x = [ex + e-x]/2
Graph : y = cosh x
Hyperbolic Cosine Function

5. Hyperbolic Function Example

6. A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with
the resultant, operates and reaches back to the original function.
The Inverse function
If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) =
x. A function that consists of its inverse fetches the original
value.
Example: f(x) = 2x + 5 = y
Then, g(y) = (y-5)/2 = x is the inverse of f(x).
Inverse Functions Example

7. SUM Function
The SUM function is categorized under Excel Math and Trigonometry functions. The function will sum up cells that are supplied as
multiple arguments. It is the most popular and widely used function in Excel.
Formula
=SUM(number1, [number2], [number3]……)
The SUM function uses the following arguments:
1.Number1 (required argument) – This is the first item that we wish to sum.
2.Number2 (required argument) – The second item that we wish to sum.
3.Number3 (optional argument) – This is the third item that we wish to sum.
The function sums values supplied as arguments (up to 255 arguments). Arguments can be supplied as numbers, cell references,
ranges, arrays, constants, and the results of other formulas or functions.

8. 1. Trigonometry, Definition, Formulas, Ratios, & Identities || By: Raymond Walter Barnard.
https://www.britannica.com/science/trigonometry
2. Hyperbolic Function (Definition, Formulas, Properties, Example) (byjus.com)
https://byjus.com/maths/hyperbolic-function/
3. Inverse Function (Definition and Examples) (byjus.com)
https://byjus.com/maths/inverse-functions/#definition
4. SUM Function - Formula, Examples, How to Use SUM (corporatefinanceinstitute.com)
https://corporatefinanceinstitute.com/resources/excel/functions/sum-function/
References