Converting Angles from Degrees to Radians using MATLAB’s deg2rad() Function

Have you ever wondered how to convert an angle measured in degrees to radians? Mathematical operations such as trigonometry often require angle measurements in radians.

Radians are used extensively in advanced physics concepts, such as calculus, differential equations, and mechanics. Converting between degrees and radians can, at times, be a little cumbersome.

Fortunately, MATLAB makes this task straightforward using the built-in function “deg2rad()”. In this article, we will look at how to use the deg2rad() function and some examples of how it works.

## Syntax of the deg2rad() function

The deg2rad() function, as the name implies, converts an angle in degrees to radians. The syntax of the function is straightforward and has the form:

– output_variables = deg2rad(input_variable)

The “input_variable” parameter can be a scalar, vector, matrix or array of any dimension.

The output is an angle in radians, having the same data type and dimensions as the input variable. Conversion of scalar, vector, matrix or array of any dimension

MATLAB allows us to use the deg2rad() function to convert an angle in degrees to radians without worrying about the dimension of the input variable.

We can use deg2rad() on a scalar, vector, matrix or an array of any dimension. Here are some examples:

** Scalar inputs:**

>> deg2rad(90)

ans =

1.5708

** Vector inputs:**

>> deg2rad([0, 45, 90, 180, 270, 360])

ans =

0 0.7854 1.5708 3.1416 4.7124 6.2832

** Matrix inputs:**

>> deg2rad([60,30;45,15])

ans =

1.0472 0.5236

0.7854 0.2618

** Higher-dimensional array inputs:**

>> x = rand([3,3,2,2,4]) * 360

x(:,:,1,1,1) =

235.9153 246.0429 178.5874

102.7044 184.7819 24.3334

118.3144 347.2303 307.9971

>> deg2rad(x)

ans(:,:,1,1,1) =

4.1148 4.2848 3.1174

1.7920 3.2207 0.4247

2.0627 6.0601 5.3731

## Output variable having the same data type and size as the input variable

The output variable of the deg2rad() function has the same data type and size as the input variable. This means that if the input variable is a scalar, the output variable will also be a scalar.

Similarly, if the input variable is a vector, the output variable will be a vector of the same size. The same is true for matrices and arrays of any dimension.

This property of the deg2rad() function helps us to avoid any unexpected changes to the dimensions of the input variable during the conversion process.

## Comparison with degtorad() function and limitations

Besides the deg2rad() function, MATLAB also has a degtorad() function. Both functions perform the same task, i.e., converting an angle in degrees to radians.

The primary difference between them is that deg2rad() is a built-in function in MATLAB, while degtorad() is a function from the Mapping Toolbox. Another difference is that deg2rad() can handle inputs of any data type, while degtorad() only works with inputs of a “double” data type.

An important limitation of the deg2rad() function is that it only works on input angles in the range of -180 to 180 degrees. If we try to use the deg2rad() function on angles outside this range, we will obtain an error message.

## Example of Converting an Angle in Degrees to Radians using deg2rad() Function

To illustrate how to use the deg2rad() function, let us convert 90 degrees to radians. The MATLAB script for this would be:

>> deg2rad(90)

## The output would be:

ans =

1.5708

In this example, our input angle was 90 degrees, and our output was 1.5708 radians.

## Conclusion

In conclusion, the deg2rad() function in MATLAB provides a convenient way to convert angles measured in degrees to radians. The use of this built-in function is simple and straightforward and works on scalar, vector, matrix or an array of any dimension.

Remember to use deg2rad() for inputs within the range of -180 to 180 degrees. With the help of this function, we can perform mathematical operations involving angles in radians without worrying about the conversion to radians.

In this article, we have explored how to convert angles measured in degrees to radians using MATLAB’s deg2rad() function. We began by introducing the syntax of the function, which takes an input angle in degrees and returns the corresponding value in radians.

We also discussed how the deg2rad() function can be used on scalar, vector, matrix, or an array of any dimension, retaining the same data type and size for the output. One of the essential features of the deg2rad() function is that the output has the same data type and size as the input.

This is crucial in preserving the structure of the input variable, preventing warnings and errors during the conversion process. Additionally, we noted that this flexibility allows us to avoid unnecessary data type conversions, a factor that can impact the performance of our code.

In comparison to the degtorad() function, also available in MATLAB, deg2rad() is more versatile because it can handle inputs of any data type and can be employed more extensively without requiring the Mapping Toolbox to be installed. However, it is important to note the limitations of the deg2rad() function, which works only on input angles within the range of -180 to 180 degrees.

Now let us dive deeper into some additional properties of the deg2rad() function to appreciate its importance further.

## Handling complex numbers

In addition to handling inputs of any data type, the deg2rad() function can convert complex-valued angles from degrees to radians. Consider the following example:

>> deg2rad(90 + 45i)

ans =

1.5708 + 0.7854i

This output shows that the deg2rad() function can handle complex inputs by performing the conversion in the real and imaginary parts of the angle separately.

This feature can be especially helpful when working with complex trigonometric functions or complex numbers expressed in polar form.

## Speed advantage

The deg2rad() function is a built-in function in MATLAB and, as such, operates faster than other user-defined functions that perform the same operation. By using the deg2rad() function, we can significantly reduce the time taken to convert angles in degrees to radians, especially for high-performance computing or large datasets.

## Using the function within user-defined functions

The deg2rad() function can be called from within user-defined functions, making it possible to automate the conversion of angles measured in degrees to radians. Consider the example of a simple trigonometric function that computes the sine of an angle in degrees:

function y = deg_sin(x)

radians = deg2rad(x);

y = sin(radians);

end

In this code, the deg_sin() function receives an input angle in degrees and calls the deg2rad() function to convert it to radians.

The result is then fed to the sine function, and the output is returned as the function’s output. Here, the deg2rad() function plays a crucial role in seamlessly integrating the conversion process within the custom-built function.

## Using a vectorized notation

The deg2rad() function can also be used with MATLAB’s vectorized notation to convert multiple angles in degrees to radians simultaneously. To do this, we pass an array of angles in degrees as the input variable.

The resultant output will be of the same size and data type as the input variable. For instance:

>> deg2rad([45 90 135 180])

ans =

0.7854 1.5708 2.3562 3.1416

This example shows that the deg2rad() function converted all the angles within the input vector to their corresponding values in radians.

In conclusion, using the deg2rad() function in MATLAB is an effective and straightforward method for converting angles measured in degrees to radians. It offers flexibility in data types and sizes, can handle complex-valued inputs, and is faster than equivalent user-defined functions.

We also note that the deg2rad() function can be integrated into user-defined functions, used with vectorized notation, and gives precise output values for any given input. By understanding the behavior and limitations of this powerful function, we can improve the robustness and efficiency of our code and reduce the possibility of errors.

In this article, we explored MATLAB’s deg2rad() function and how it can be used to convert angles measured in degrees to radians. We saw that the function has a simple syntax, can handle inputs of any data type, and provides output values of the same data type and size as the input.

Additionally, we noted that deg2rad() is faster than user-defined functions, can handle complex-valued inputs, and can be integrated into user-defined functions. Our key takeaway is that understanding the behavior and limits of this function can help us write efficient, robust code, especially when working with mathematical operations that require angles in radians.