Python math.asin() Method

The Python math.asin() method is used to compute the arc sine of an angle, in radians.

The arc sine of an angle is defined as the inverse of a sine function. Therefore, the domain of the arc sine function is the range of the sine function, i.e., [-1, 1]; and its range is obtained in the form of radians. They can be converted into degrees using the degrees() method, if required.

Note − This function is not accessible directly, so we need to import math module and then we need to call this function using math static object.

Syntax

Following is the syntax for the Python math.asin() method −

math.asin(x)

Parameters

  • x − This must be a numeric value in the range -1 to 1. If x is greater than 1 then it will generate an error.

Return Value

This method returns arc sine of x, in radians.

Example

The following example shows the usage of the Python math.asin() method. In here, we are trying to find the arc sine values for the standard sine values '0', '-1', and '1' using this method.

import math

zero = math.asin(0)
neg_one = math.asin(-1)
pos_one = math.asin(1)

print("Arc Sine value of 0:", zero)
print("Arc Sine value of -1:", neg_one)
print("Arc Sine value of 1:", pos_one)

When we run above program, it produces following result −

Arc Sine value of 0: 0.0
Arc Sine value of -1: -1.5707963267948966
Arc Sine value of 1: 1.5707963267948966

Example

Now let us try to convert the return values obtained from the method in the previous example into degrees using the degrees() method.

In this example, three objects containing the values 0, -1 and 1 are created. Using the asin() method, the arc sine values of these objects are calculated in radians; which are later converted into degrees using the degrees() method.

import math

zero = math.asin(0)
neg_one = math.asin(-1)
pos_one = math.asin(1)

print("Arc Sine value of 0:", math.degrees(zero))
print("Arc Sine value of -1:", math.degrees(neg_one))
print("Arc Sine value of 1:", math.degrees(pos_one))

Once the program is executed, the output is produced as follows −

Arc Sine value of 0: 0.0
Arc Sine value of -1: -90.0
Arc Sine value of 1: 90.0

Example

The following example passes non-standard sine ratios as arguments to this method; then the arc sine values for these objects are calculated.

import math

asin1 = math.asin(0.57)
asin2 = math.asin(-0.33)

print("Arc Sine value of 0.57:", asin1)
print("Arc Sine value of -0.33:", asin2)

On compiling and executing the program above, the result is displayed as follows −

Arc Sine value of 0.57: 0.6065058552130869
Arc Sine value of -0.33: -0.33630357515398035

Example

However, if the arguments passed to this method exceed the value 1 or precede -1, a ValueError is raised.

import math

asin1 = math.asin(2)
asin2 = math.asin(-2)

print("Arc Sine value of 2:", asin1)
print("Arc Sine value of -2:", asin2)

If we compile and run the program, the output is produced as follows −

Traceback (most recent call last):
  File "main.py", line 3, in 
acos1 = math.asin(2)
ValueError: math domain error
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