Matlab Calculate in Degrees

Introduction to MATLAB Degree Calculations

MATLAB uses radians as its default unit for trigonometric functions. However, many real-world applications use degrees. To work with degrees in MATLAB, you need to understand how to convert between degrees and radians, and how to perform calculations using degree-based inputs.

The key functions for degree calculations in MATLAB include deg2rad, rad2deg, and the trigonometric functions with degree inputs. These functions allow you to seamlessly work with angles in degrees while MATLAB handles the underlying radian calculations.

Basic MATLAB Functions for Degrees

Converting Between Degrees and Radians

MATLAB provides two essential functions for converting between degrees and radians:

• deg2rad(d) - Converts degrees to radians
• rad2deg(r) - Converts radians to degrees

Trigonometric Functions with Degree Inputs

MATLAB's trigonometric functions can accept degree inputs by using the d suffix:

• sind(x) - Sine of x in degrees
• cosd(x) - Cosine of x in degrees
• tand(x) - Tangent of x in degrees
• asind(x) - Arcsine of x in degrees
• acosd(x) - Arccosine of x in degrees
• atand(x) - Arctangent of x in degrees

Converting Between Degrees and Other Units

In addition to radians, you may need to convert between degrees and other angle units:

Degrees to Gradians

Gradians are another unit of angle measurement where a full circle is 400 gradians.

Degrees to Minutes and Seconds

Degrees can be further divided into minutes and seconds:

• 1 degree = 60 minutes
• 1 minute = 60 seconds

Trigonometric Calculations in Degrees

Performing trigonometric calculations in degrees requires using the degree-specific functions mentioned earlier. Here's how to use them effectively:

Calculating Sine, Cosine, and Tangent

To calculate the sine of 30 degrees:

> sind(30)
ans =
    0.5000

To calculate the cosine of 60 degrees:

> cosd(60)
ans =
    0.5000

Inverse Trigonometric Functions

To find the angle whose sine is 0.5:

> asind(0.5)
ans =
   30

To find the angle whose tangent is 1:

> atand(1)
ans =
   45

Practical Examples

Example 1: Converting Degrees to Radians

Convert 45 degrees to radians:

> deg2rad(45)
ans =
    0.7854

Example 2: Calculating the Hypotenuse

Given a right triangle with angles 30° and 60°, calculate the hypotenuse if one side is 1:

> hypotenuse = 1 / sind(30)
hypotenuse =
    2.0000

Example 3: Solving a Triangle

Given a triangle with sides 3, 4, and angle between them 90°, find the third side:

> c = sqrt(3^2 + 4^2 - 2*3*4*cosd(90))
c =
    5.0000