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# Python - math.acos() method example

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The `math.acos` function returns number in radians in the range `0` to `math.pi`. Based on this function we are able to calculate the inverted cosine function value.

``````import math

print(math.acos(-2))    # NaN
print(math.acos(-1))    # 3.1415926535897930 ->  180
print(math.acos(-0.5))  # 2.0943951023931957 -> ~120
print(math.acos(0))     # 1.5707963267948966 ->   90
print(math.acos(0.5))   # 1.0471975511965979 ->  ~60
print(math.acos(1))     # 0                  ->    0
print(math.acos(2))     # NaN

print(math.acos(0.7071067811865476))  # 0.7853981633974483 -> 45 deg
print(math.acos(0.8660254037844387))  # 0.5235987755982987 -> 30 deg

print(math.acos(math.cos(math.pi / 4)))  # 0.7853981633974483 -> pi/4 (45deg)
print(math.cos(math.cos(math.pi / 4)))   # 0.7853981633974483 -> pi/4 (45deg)``````

Another way to look at `acos` function:

``````import math

def calculateAngle(b, h):
return math.acos(b / h)

#   |\
#   | \ h
# a |  \
#   |__*\ <- angle
#     b

# a, b and h build isosceles right triangle
a = 3
b = a
h = math.sqrt(a * a + b * b)
print(calculateAngle(b, h))  # 0.7853981633974483 <-  45 degrees

# a, b and h build half of equilateral triangle
a = 3
b = a * math.sqrt(3)
h = math.sqrt(a * a + b * b)
print(calculateAngle(b, h))  # 0.5235987755982987 <- ~30 degrees

# a, b and h are not able to build triangle
a = 3
b = a
h = 1
print(calculateAngle(b, h))  # ValueError``````

## 1. Documentation

 Syntax ``math.acos(number)`` Parameters `number` - a value that represents the result of the operation `adjacent / hypotenuse` on the right triangle. `number` should be in the range `-1` to `+1`. Result `number` value in radians in the range `0` to `math.pi`. If the value can not be calculated `ValueError` occurs. Description `acos` is a method that takes only one parameter and returns an approximation of the result of the mathematical function arccosine(x).

## 2. Working with degrees

``````import math

def calculateAngle(b, h):
return math.acos(b / h)

#   |\
#   | \ h
# a |  \
#   |__*\ <- angle
#     b

# a, b and h build isosceles right triangle
a = 3
b = a
h = math.sqrt(a * a + b * b)
print(calculateAngle(b, h))  # 0.7853981633974483 <-  45 degrees

# a, b and h build half of equilateral triangle
a = 3
b = a * math.sqrt(3)
h = math.sqrt(a * a + b * b)
print(calculateAngle(b, h))  # 0.5235987755982987 <- ~30 degrees

# a, b and h are not able to build triangle
a = 3
b = a
h = 1
print(calculateAngle(b, h))  # ValueError``````

## References

1. Inverse trigonometric functions - Wikipedia