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Problem Solutions

## The `math` Module

The `math` module is made available to your programs with:

```import math
```

The `math` module contains the following trigonometric functions

`math.acos `( `x` ) → number

arc cosine of x .

`math.asin `( `x` ) → number

arc sine of x .

`math.atan `( `x` ) → number

arc tangent of x .

`math.atan2 `( `y` , `x` ) → number

arc tangent of y / x .

`math.cos `( `x` ) → number

cosine of x .

`math.cosh `( `x` ) → number

hyperbolic cosine of x .

`math.exp `( `x` ) → number

e** x , inverse of log( x ).

`math.hypot `( `x` , `y` ) → number

Euclidean distance, sqrt( x * x + y * y ), length of the hypotenuse of a right triangle with height of y and length of x .

`math.log `( `x` ) → number

natural logarithm (base e) of x , inverse of exp( x ).

`math.log10 `( `x` ) → number

natural logarithm (base 10) of x , inverse of 10** x .

`math.pow `( `x` , `y` ) → number

x ** y .

`math.sin `( `x` ) → number

sine of x .

`math.sinh `( `x` ) → number

hyperbolic sine of x .

`math.sqrt `( `x` ) → number

square root of x . This version returns an error if you ask for sqrt(-1), even though Python understands complex and imaginary numbers. A second module, `cmath`, includes a version of `sqrt`( `x` ) which correctly creates imaginary numbers.

`math.tan `( `x` ) → number

tangent of x .

`math.tanh `( `x` ) → number

hyperbolic tangent of x .

Additionally, the following constants are also provided.

`math.pi`

the value of pi, 3.1415926535897931

`math.e`

the value of e, 2.7182818284590451, used for the `exp`( `x` ) and `log`( `x` ) functions.

The math module contains the following other functions for dealing with floating point numbers.

`math.ceil `( `x` ) → number

next larger whole number. `math.ceil(5.1) == 6`, `math.ceil(-5.1) == -5.0`.

`math.fabs `( `x` ) → number

absolute value of the real x .

`math.floor `( `x` ) → number

next smaller whole number. `math.floor(5.9) == 5`, `math.floor(-5.9) == -6.0`.

`math.fmod `( `x` , `y` ) → number

floating point remainder after division of x / y . This depends on the platform C library and may return a different result than the Python `x % y`.

`math.modf `( `x` ) → ( number, number )

creates a tuple with the fractional and integer parts of x . Both results carry the sign of x so that x can be reconstructed by adding them.

`math.frexp `( `x` ) → ( number, number )

this function unwinds the usual base-2 floating point representation. A floating point number is m *2** e , where m is always a fraction between 1/2 and 1, and e is an integer power of 2. This function returns a tuple with m and e . The inverse is `ldexp(m,e)`.

`math.ldexp `( `m` , `e` ) → number

m *2** e , the inverse of `frexp(x)`.

 Published under the terms of the Open Publication License Design by Interspire