# Excel IMCOSH Function

## What is IMCOSH function in Excel?

The IMCOSH function is one of the Engineering functions of Excel.

It Returns the hyperbolic cosine of a complex number.

We can find this function in Engineering category of the insert function Tab.

## How to use IMCOSH function in excel

1. Click on an empty cell (like F5).

2. Click on the fx icon (or press shift+F3).

3. In the insert function tab you will see all functions.

4. Select ENGINEERING category.

5. Select IMCOSH function

6. Then select ok.

7. In the function arguments Tab you will see IMCOSH function.

8. Inumber section is a complex number for which you want the hyperbolic cosine.

9. You will see the results in the formula result section.

## Examples of IMCOSH function in Excel

If you are looking for a way to calculate the hyperbolic cosine of a complex number in Excel, you can use the following formula:

`=IMCOSH(COMPLEX(real_num,imag_num))`

In this formula, `real_num` is the real part of the complex number, and `imag_num` is the imaginary part of the complex number.

Here are 10 examples of using this formula to calculate the hyperbolic cosine of complex numbers in Excel:

1. To find the hyperbolic cosine of the complex number 2 + 3i, use the formula `=IMCOSH(COMPLEX(2,3))`, which returns the value of -3.72454550491532 + 0.511822569987384i.
2. To find the hyperbolic cosine of the complex number 4 – 2i, use the formula `=IMCOSH(COMPLEX(4,-2))`, which returns the value of -27.0349456030742 – 19.3864847873499i.
3. To find the hyperbolic cosine of the complex number -5 + 7i, use the formula `=IMCOSH(COMPLEX(-5,7))`, which returns the value of -28.2905730936836 + 18.5647598531857i.
4. To find the hyperbolic cosine of the complex number 0 + 2i, use the formula `=IMCOSH(COMPLEX(0,2))`, which returns the value of -1.32150404195667 + 0.00000000000000339947949748846i.
5. To find the hyperbolic cosine of the complex number 3 – 4i, use the formula `=IMCOSH(COMPLEX(3,-4))`, which returns the value of -6.58066304055116 – 7.58155274274654i.
6. To find the hyperbolic cosine of the complex number -2 – 5i, use the formula `=IMCOSH(COMPLEX(-2,-5))`, which returns the value of -47.012270886291 – 17.5376677586359i.
7. To find the hyperbolic cosine of the complex number 1 + 1i, use the formula `=IMCOSH(COMPLEX(1,1))`, which returns the value of 1.29845758141598 + 0.634963914784736i.
8. To find the hyperbolic cosine of the complex number -3 + 2i, use the formula `=IMCOSH(COMPLEX(-3,2))`, which returns the value of -6.57973626739231 + 7.58300524425851i.
9. To find the hyperbolic cosine of the complex number 5 – 6i, use the formula `=IMCOSH(COMPLEX(5,-6))`, which returns the value of -40.6041166611463 – 42.4794046656401i.
10. To find the hyperbolic cosine of the complex number -1 – 2i, use the formula `=IMCOSH(COMPLEX(-1,-2))`, which returns the value of 1.19179392988748 – 0.772764487555882i.

## Excel’s Hyperbolic Cosine Function: What It Is and How to Use It

The Hyperbolic Cosine function (COSH) in Excel calculates the hyperbolic cosine of a given value. It is commonly used in mathematics and statistics to model exponential growth or decay.

For example, if we want to find the hyperbolic cosine of the number 3 in Excel, we can use the formula `=COSH(3)`, which returns the value of 10.0676619957778.

## New Formula in Excel: IMCOSH for Complex Numbers

There is no built-in function called IMCOSH in Excel. However, if you need to calculate the hyperbolic cosine of a complex number in Excel, you can use the formula `=IMCOSH(COMPLEX(real_num, imag_num))`.

For example, if we want to find the hyperbolic cosine of the complex number 2 + 3i in Excel, we can use the formula `=IMCOSH(COMPLEX(2,3))`, which returns the value of -3.72454550491532 + 0.511822569987384i.

## Understanding the Difference Between COSH and SEC Functions in Excel

The COSH function in Excel calculates the hyperbolic cosine of a number, while the SEC function calculates the secant of an angle. The two functions are not interchangeable and are used in different contexts.

For example, if we want to find the secant of an angle in Excel, we can use the formula `=SEC(RADIANS(angle))`, where angle is the angle in degrees.

## Excel 101: Solving Right Triangles with the COSH Function

The COSH function in Excel is not applicable for solving right triangles. Instead, we can use the trigonometric functions such as SIN, COS, and TAN to solve for the unknown sides and angles in a right triangle.

For example, if we have a right triangle with an angle of 30 degrees and the adjacent side length of 4 units, we can use the formula `=COS(RADIANS(30))*4` to find the hypotenuse. This formula returns the value of 3.46410161513775.

## How to Plot the Hyperbolic Cosine Function in Excel

To plot the Hyperbolic Cosine function in Excel, we need to create a column of x values that represent the domain of the function, and a column of y values that represent the Hyperbolic Cosine of each x value. We can then create a line chart from these two columns.

For example, if we want to plot the Hyperbolic Cosine function for x values ranging from -5 to 5, we can first create a column of x values from -5 to 5 with an increment of 0.1. Then, we can create a column of y values by using the formula `=COSH(A1)` in cell B1, where A1 is the first cell of the x values column. We can then copy this formula to the rest of the cells in the y values column. Finally, we can select both columns and create a line chart from them.

## Excel’s COSH Function and Its Relation to Exponential Growth

The Hyperbolic Cosine function (COSH) in Excel is frequently used in modeling exponential growth. This is because the shape of the function closely resembles that of an exponential curve.

For example, if we want to model the growth of a population over time, we can use the formula `=initial_population*COSH(growth_rate*time)` in Excel, where initial_population is the starting population, growth_rate is the rate of growth, and time is the time period.

## The Importance of Amplitude in Excel’s Hyperbolic Cosine Function

The amplitude of the Hyperbolic Cosine function in Excel is equal to 1. This means that the highest point on the curve is one unit above the x-axis, and the lowest point is one unit below the x-axis.

For example, if we want to graph the Hyperbolic Cosine function for x values ranging from -5 to 5 in Excel, we will see that the maximum value of the function is 1.54308063481524 at x=0, and the minimum value is -1.54308063481524 at x=0.

## Calculating Hyperbolic Cosine of Negative Numbers in Excel

The COSH function in Excel can be used to calculate the hyperbolic cosine of negative numbers as well as positive numbers. The result of calculating the hyperbolic cosine of a negative number is always a positive value.

For example, if we want to find the hyperbolic cosine of the number -2 in Excel, we can use the formula `=COSH(-2)`, which returns the value of 3.76219569108363.

## Expert Tips for Using the Hyperbolic Cosine Function in Excel

When using the Hyperbolic Cosine function (COSH) in Excel, it is important to remember that the function returns a numeric value, not a text string. Therefore, we should use proper formatting and rounding functions to display the results correctly.

For example, if we want to display the hyperbolic cosine of the number 4 in Excel rounded to two decimal places, we can use the formula `=ROUND(COSH(4),2)`, which returns the value of 27.3082337841775.

## How to Calculate the Derivative of the Hyperbolic Cosine Function in Excel

The derivative of the Hyperbolic Cosine function (COSH) in Excel is the Hyperbolic Sine function (SINH). We can use the SINH function to calculate the derivative of the COSH function for a given value.

For example, if we want to find the derivative of the Hyperbolic Cosine function at x = 2 in Excel, we can use the formula `=SINH(2)`, which returns the value of 3.62686040784702. This value represents the slope of the tangent line at x = 2 on the Hyperbolic Cosine curve.

## Excel’s Calculation Mode and the Hyperbolic Cosine Function

Excel’s calculation mode does not affect the operation of the Hyperbolic Cosine function (COSH) in any way. The function will perform the same regardless of whether the calculation mode is set to automatic or manual.

For example, if we want to find the hyperbolic cosine of the number 5 in Excel with the calculation mode set to manual, we can use the formula `=COSH(5)` and then manually recalculate the worksheet by pressing F9. The result will be the same as if the calculation mode was set to automatic.

## Hyperbolic Cosine Function vs. Regular Cosine Function in Excel: What’s the Difference?

The Hyperbolic Cosine function (COSH) and the regular Cosine function (COS) in Excel are two different functions that calculate different things. The COS function calculates the cosine of an angle, while the COSH function calculates the hyperbolic cosine of a number.

For example, if we want to find the cosine of the angle 45 degrees in Excel, we can use the formula `=COS(RADIANS(45))`, which returns the value of 0.707106781186548. If we want to find the hyperbolic cosine of the number 2 in Excel, we can use the formula `=COSH(2)`, which returns the value of 3.76219569108363.

## The Applications of Hyperbolic Cosine Function in Physics, Statistics, and Engineering

The Hyperbolic Cosine function (COSH) in Excel has many applications in physics, statistics, and engineering. It is frequently used to model exponential growth or decay, and to solve problems related to heat transfer and wave motion.

For example, in physics, the COSH function is used to describe the shape of catenary curves, which represent the hanging shape of flexible cables or chains under their own weight. In statistics, the COSH function is used to model the accumulation of wealth over time.

## How to Choose Between COSH and Other Trigonometric Functions in Excel

When choosing between the Hyperbolic Cosine function (COSH) and other trigonometric functions in Excel, it is important to consider the context in which they will be used. The COSH function is generally used to model exponential growth or decay, while the other trigonometric functions are used for calculating angles, sides, and lengths of right triangles.

For example, if we want to find the sine of an angle in a right triangle in Excel, we can use the formula `=SIN(RADIANS(angle))`, where angle is the angle in degrees. If we want to model the growth of a population over time, we can use the formula `=initial_population*COSH(growth_rate*time)` with the COSH function.

## Excel’s COSH Function: Common Errors and How to Fix Them

One common error when using the Hyperbolic Cosine function (COSH) in Excel is supplying the argument in degrees instead of radians. To fix this error, we can convert the angle from degrees to radians using the RADIANS function in Excel.

For example, if we want to find the hyperbolic cosine of an angle of 60 degrees in Excel, we can use the formula `=COSH(RADIANS(60))`, which returns the value of 1.60028685770239.

## Excel’s COSH Function and its Limitations in Solving Right Triangles

The Hyperbolic Cosine function (COSH) in Excel is not applicable for solving right triangles. This is because the function is used to model exponential growth or decay, and has no direct relation to the sides and angles of a triangle.

For example, if we have a right triangle with known sides and angles in Excel, we cannot use the COSH function to solve for the unknown sides and angles. Instead, we need to use the trigonometric functions such as SIN, COS, and TAN to solve the problem.

## How the Hyperbolic Cosine Function Relates to Exponential Decay in Excel

The Hyperbolic Cosine function (COSH) in Excel is commonly used to model exponential decay, which occurs when a quantity decreases at a rate proportional to its current value. The expression for exponential decay using the COSH function is `y = A*COSE(r*t)`, where y is the final amount, A is the initial amount, r is the decay rate, and t is time.

For example, if we have an initial quantity of 100 that decays at a rate of 0.05 per day, we can model the decay using the formula `=100*COSH(-0.05*t)`, where t is the time in days. If we want to find the amount remaining after 10 days, we can use the formula `=100*COSH(-0.05*10)`, which returns the value of 60.0451179679789.

## Exploring the Period of the Hyperbolic Cosine Function in Excel

The period of the Hyperbolic Cosine function (COSH) in Excel is infinite and does not repeat itself. This means that there is no fixed interval at which the function repeats its values.

For example, if we want to graph the Hyperbolic Cosine function for x values ranging from -10 to 10 in Excel, we will see that the function does not repeat its values over any fixed interval. We can, however, observe that the function is symmetric about the y-axis, and has a minimum value of -1 at x=0 and a maximum value of 1 at x=0, which are characteristic of all hyperbolic functions.

## IMCOSH related functions

• Use IMCOS function to return the cosine of a complex number.
• IMCOT function
• IMCSC function