Updated On : Jul-15,2020 Time Investment : ~10 mins

# Learning NumPy - Mathematical Functions - Part 14¶

Quite understandably, NumPy contains a large number of various mathematical operations. NumPy provides standard trigonometric functions, functions for arithmetic operations, handling complex numbers, etc.

Trigonometric Functions NumPy has standard trigonometric functions which return trigonometric ratios for a given angle in radians.

### Example¶

```import numpy as np
a = np.array([0,30,45,60,90])

print ('Sine of different angles:')
# Convert to radians by multiplying with pi/180
print (np.sin(a*np.pi/180))
print ('\n')

print ('Cosine values for angles in array:')
print (np.cos(a*np.pi/180))
print ('\n')

print ('Tangent values for given angles:')
print (np.tan(a*np.pi/180))
```
```Sine of different angles:
[0.         0.5        0.70710678 0.8660254  1.        ]

Cosine values for angles in array:
[1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01
6.12323400e-17]

Tangent values for given angles:
[0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00
1.63312394e+16]
```

### Point To Understand¶

• arcsin, arcos, and arctan functions return the trigonometric inverse of sin, cos, and tan of the given angle. The result of these functions can be verified by numpy.degrees() function by converting radians to degrees.
```import numpy as np
a = np.array([0,30,45,60,90])

print ('Array containing sine values:')
sin = np.sin(a*np.pi/180)
print (sin)
print ('\n')

print ('Compute sine inverse of angles. Returned values are in radians.')
inv = np.arcsin(sin)
print (inv)
print ('\n')

print ('Check result by converting to degrees:')
print (np.degrees(inv))
print ('\n')

print ('arccos and arctan functions behave similarly:')
cos = np.cos(a*np.pi/180)
print (cos)
print ('\n')

print ('Inverse of cos:')
inv = np.arccos(cos)
print (inv)
print ('\n')

print ('In degrees:')
print (np.degrees(inv))
print ('\n')

print ('Tan function:')
tan = (np.tan(a*np.pi/180))
print (tan)
print ('\n')

print ('Inverse of tan:')
inv = (np.arctan(tan))
print (inv)
print ('\n')

print ('In degrees:')
print (np.degrees(inv))
```
```Array containing sine values:
[0.         0.5        0.70710678 0.8660254  1.        ]

Compute sine inverse of angles. Returned values are in radians.
[0.         0.52359878 0.78539816 1.04719755 1.57079633]

Check result by converting to degrees:
[ 0. 30. 45. 60. 90.]

arccos and arctan functions behave similarly:
[1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01
6.12323400e-17]

Inverse of cos:
[0.         0.52359878 0.78539816 1.04719755 1.57079633]

In degrees:
[ 0. 30. 45. 60. 90.]

Tan function:
[0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00
1.63312394e+16]

Inverse of tan:
[0.         0.52359878 0.78539816 1.04719755 1.57079633]

In degrees:
[ 0. 30. 45. 60. 90.]
```

### Functions for Rounding¶

numpy.around()

This is a function that returns the value rounded to the desired precision. The function takes the following parameters.

```numpy.around(a,decimals)
```
Parameter Description
a Input data
decimals The number of decimals to round to. Default is 0. If negative, the integer is rounded to position to the left of the decimal point

### Example 1¶

```import numpy as np
a = np.array([1.0,5.55, 123, 0.567, 25.532])

print ('Original array:')
print (a)
print ('\n')

print ('After rounding:')
print (np.around(a))
print (np.around(a, decimals = 1))
print (np.around(a, decimals = -1))
```
```Original array:
[  1.      5.55  123.      0.567  25.532]

After rounding:
[  1.   6. 123.   1.  26.]
[  1.    5.6 123.    0.6  25.5]
[  0.  10. 120.   0.  30.]
```

### numpy.floor()¶

This function returns the largest integer not greater than the input parameter. The floor of the scalar x is the largest integer i, such that i <= x. Note that in Python, flooring always is rounded away from 0.

```import numpy as np
a = np.array([-1.7, 1.5, -0.2, 0.6, 10])

print ('The given array:')
print (a)
print ('\n')

print ('The modified array:')
print (np.floor(a))
```
```The given array:
[-1.7  1.5 -0.2  0.6 10. ]

The modified array:
[-2.  1. -1.  0. 10.]
```

### numpy.ceil()¶

The ceil() function returns the ceiling of an input value, i.e. the ceil of the scalar x is the smallest integer i, such that i >= x.

```import numpy as np
a = np.array([-1.7, 1.5, -0.2, 0.6, 10])

print ('The given array:')
print (a)
print ('\n')

print ('The modified array:')
print (np.ceil(a))
```
```The given array:
[-1.7  1.5 -0.2  0.6 10. ]

The modified array:
[-1.  2. -0.  1. 10.]
```
Dolly Solanki

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