# Python Language Math Module Trigonometry

## Example

### Calculating the length of the hypotenuse

``````math.hypot(2, 4) # Just a shorthand for SquareRoot(2**2 + 4**2)
# Out: 4.47213595499958
``````

All `math` functions expect radians so you need to convert degrees to radians:

``````math.radians(45)              # Convert 45 degrees to radians
# Out: 0.7853981633974483
``````

All results of the inverse trigonometic functions return the result in radians, so you may need to convert it back to degrees:

``````math.degrees(math.asin(1))    # Convert the result of asin to degrees
# Out: 90.0
``````

### Sine, cosine, tangent and inverse functions

``````# Sine and arc sine
math.sin(math.pi / 2)
# Out: 1.0
math.sin(math.radians(90))   # Sine of 90 degrees
# Out: 1.0

math.asin(1)
# Out: 1.5707963267948966    # "= pi / 2"
math.asin(1) / math.pi
# Out: 0.5

# Cosine and arc cosine:
math.cos(math.pi / 2)
# Out: 6.123233995736766e-17
# Almost zero but not exactly because "pi" is a float with limited precision!

math.acos(1)
# Out: 0.0

# Tangent and arc tangent:
math.tan(math.pi/2)
# Out: 1.633123935319537e+16
# Very large but not exactly "Inf" because "pi" is a float with limited precision
``````
Python 3.x3.5
``````math.atan(math.inf)
# Out: 1.5707963267948966 # This is just "pi / 2"
``````
``````math.atan(float('inf'))
# Out: 1.5707963267948966 # This is just "pi / 2"
``````

Apart from the `math.atan` there is also a two-argument `math.atan2` function, which computes the correct quadrant and avoids pitfalls of division by zero:

``````math.atan2(1, 2)   # Equivalent to "math.atan(1/2)"
# Out: 0.4636476090008061 # ≈ 26.57 degrees, 1st quadrant

math.atan2(-1, -2) # Not equal to "math.atan(-1/-2)" == "math.atan(1/2)"
# Out: -2.677945044588987 # ≈ -153.43 degrees (or 206.57 degrees), 3rd quadrant

math.atan2(1, 0)   # math.atan(1/0) would raise ZeroDivisionError
# Out: 1.5707963267948966 # This is just "pi / 2"
``````

### Hyperbolic sine, cosine and tangent

``````# Hyperbolic sine function
math.sinh(math.pi) # = 11.548739357257746
math.asinh(1)      # = 0.8813735870195429

# Hyperbolic cosine function
math.cosh(math.pi) # = 11.591953275521519
math.acosh(1)      # = 0.0

# Hyperbolic tangent function
math.tanh(math.pi) # = 0.99627207622075
math.atanh(0.5)    # = 0.5493061443340549
`````` PDF - Download Python Language for free