Trigonometry

Trigonometry#

Overview#

The trigonometric functions for sine, cosine, and tangent (and associated inverse functions) are built-in functions in Python as well as part of a common Python package numpy

Using the math and cmath module#

The math and cmath modules are part of the Python Standard Library and require no additional downloading to use. Both math modules can be used to calculate the value of trigonometric functions in Python

Both math modules expect an input value in radians:

  • Input: single numerical values (float, decimals, integers)

  • Returns: single numerical value in radians as a float

The math function only works on real number inputs, while cmath contains equivalent functions for for complex and imaginary numbers

However, if you are working with lists or arrays we suggest using the numpy equivalents

sin#

sin calculates the sine of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_sin_value = math.sin(input_value)
print(math_sin_value)

0.479425538604203

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_sin_value = np.sin(input_value)
print(np_sin_value)

0.479425538604203

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_sin_array_values = np.sin(input_values)
print(np_sin_array_values)

[0.47942554 0.68163876 0.84147098]

cos#

cos calculates the cosine of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_cos_value = math.cos(input_value)
print(math_cos_value)

0.8775825618903728

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_cos_value = np.cos(input_value)
print(np_cos_value)

0.8775825618903728

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_cos_array_values = np.cos(input_values)
print(np_cos_array_values)

[0.87758256 0.73168887 0.54030231]

tan#

tan calculates the tangent of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_tan_value = math.tan(input_value)
print(math_tan_value)

0.5463024898437905

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_tan_value = np.tan(input_value)
print(np_tan_value)

0.5463024898437905

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_tan_array_values = np.tan(input_values)
print(np_tan_array_values)

[0.54630249 0.93159646 1.55740772]

asin#

asin calculates the arcsine of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_asin_value = math.asin(input_value)
print(math_asin_value)

0.5235987755982989

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_asin_value = np.arcsin(input_value)
print(np_asin_value)

0.5235987755982989

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_asin_array_values = np.arcsin(input_values)
print(np_asin_array_values)

[0.52359878 0.84806208 1.57079633]

acos#

acos calculates the arccosine of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_acos_value = math.acos(input_value)
print(math_acos_value)

1.0471975511965979

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_acos_value = np.arccos(input_value)
print(np_acos_value)

1.0471975511965979

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_acos_array_values = np.arccos(input_values)
print(np_acos_array_values)

[1.04719755 0.72273425 0.        ]

atan#

atan calculates the arctangent of numeric values in radians

Grab and Go#

import math

input_value = 0.5  # in radians
math_atan_value = math.atan(input_value)
print(math_atan_value)

0.4636476090008061

# Input: Single Value
import numpy as np

input_value = 0.5  # in radians
np_atan_value = np.arctan(input_value)
print(np_atan_value)

0.4636476090008061

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.0])  # in radians
np_atan_array_values = np.arctan(input_value)
print(np_atan_array_values)

0.4636476090008061

atan2#

atan calculates the arctangent of y / x in radians

import math

input_value_x = 10.0  # in radians
input_value_y = 5.0  # in radian
math_atan2_value = math.atan2(input_value_y, input_value_x)
print(math_atan2_value)

0.4636476090008061

# Input: Single Value
import numpy as np

input_value_x = 10.0  # in radians
input_value_y = 5.0  # in radian
np_atan2_value = np.arctan2(input_value_y, input_value_x)
print(np_atan2_value)

0.4636476090008061

# Input: Array
import numpy as np

input_values_x = np.array([0.5, 0.75, 10.0])  # in radians
input_values_y = np.array([1.5, 1.75, 5.0])  # in radians
np_atan2_array_values = np.arctan2(input_values_y, input_values_x)
print(np_atan2_array_values)

[1.24904577 1.16590454 0.46364761]

cosh#

cosh computes the hyperbolic cosine in radians

import math

input_value = -3.2  # in radians
math_cosh_value = math.cosh(input_value)
print(math_cosh_value)

12.28664620054386

# Input: Single Value
import numpy as np

input_value = -3.2  # in radians
np_cosh_value = np.cosh(input_value)
print(np_cosh_value)

12.28664620054386

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, -3.2])  # in radians
np_cosh_array_values = np.cosh(input_values)
print(np_cosh_array_values)

[ 1.12762597  1.29468328 12.2866462 ]

sinh#

sinh computes the hyperbolic sine in radians

import math

input_value = 1.4  # in radians
math_sinh_value = math.sinh(input_value)
print(math_sinh_value)

1.9043015014515339

# Input: Single Value
import numpy as np

input_value = 1.4  # in radians
np_sinh_value = np.sinh(input_value)
print(np_sinh_value)

1.9043015014515339

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 1.4])  # in radians
np_sinh_array_values = np.sinh(input_values)
print(np_sinh_array_values)

[0.52109531 0.82231673 1.9043015 ]

tanh#

tanh computes the hyperbolic tangent in radians

import math

input_value = 0.67  # in radians
math_tanh_value = math.tanh(input_value)
print(math_tanh_value)

0.5849798828807289

import numpy as np

input_value = 0.67  # in radians
np_tanh_value = np.tanh(input_value)
print(np_tanh_value)

0.5849798828807288

# Input: Array
import numpy as np

input_values = np.array([0.5, 0.75, 0.67])  # in radians
np_tanh_array_values = np.tanh(input_values)
print(np_tanh_array_values)

[0.46211716 0.63514895 0.58497988]

Differences from NCL#

Input and Return Types#

While the math modules (math and cmath) only accept single numerical values—like NCL—numpy can accept and return either single numerical values or array-like values.

Unlike NCL, cmath and numpy can also accept complex numbers as input values

Python Resources#