Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three basic trigonometric functions are sine, cosine, and tangent.
Python provides a built-in module called math that contains a variety of mathematical functions, including trigonometric functions. To use these functions, you need to import the math module at the beginning of your code:
Once you’ve imported the math module, you can use its trigonometric functions. Here are some of the most commonly used trigonometric functions in Python:
math.sin(x): Returns the sine of the angle x in radians.
math.cos(x): Returns the cosine of the angle x in radians.
math.tan(x): Returns the tangent of the angle x in radians.
math.radians(degrees): Converts an angle in degrees to radians.
math.asin(x): Returns the arc sine of x in radians.
math.acos(x): Returns the arc cosine of x in radians.
math.atan(x): Returns the arc tangent of x in radians.
Note that the trigonometric functions in Python work with angles in radians, not degrees. If you have an angle in degrees, you can convert it to radians using the math.radians() function.
For example, let’s say you want to find the sine of 45 degrees. First, you need to convert 45 degrees to radians using the math.radians() function:
degrees = 45
radians = math.radians(degrees)
Now that you have the angle in radians, you can use the math.sin() function to find the sine of the angle:
sin_value = math.sin(radians) print(sin_value) # Output: 0.7071067811865475
Similarly, you can use the math.cos() and math.tan() functions to find the cosine and tangent of an angle in radians.
The math.asin(), math.acos(), and math.atan() functions are used to find the inverse trigonometric functions. For example, if you have the value of the sine of an angle and you want to find the angle itself, you can use the math.asin() function.
sin_value = 0.5
arc_sin = math.asin(sin_value)
print(arc_sin) # Output: 0.5235987755982989
This returns the angle in radians. You can convert it to degrees using the math.degrees() function:
degrees = math.degrees(arc_sin)
print(degrees) # Output: 30.000000000000004
These are the basic functions and concepts used to handle trigonometry in Python.