YouTipRef Math Acos
## Python math.acos() Method
The `math.acos()` method is a built-in function in Python's standard `math` module. It returns the arc cosine (also known as the inverse cosine) of a given number.
The returned angle is expressed in radians and falls within the range $[0, \pi]$.
---
### Syntax
To use the `math.acos()` method, you must first import the `math` module:
```python
import math
math.acos(x)
```
### Parameters
| Parameter | Type | Description |
| :--- | :--- | :--- |
| `x` | `float` or `int` | **Required.** A numeric value between `-1` and `1` (inclusive). |
### Return Value
* **Type:** `float`
* **Description:** Returns the arc cosine of `x` in radians.
* **Range:** The returned value is always between `0.0` and `3.141592653589793` (which is $\pi$).
---
### Code Examples
The following example demonstrates how to use `math.acos()` with various positive, negative, and boundary values.
```python
import math
# Calculate the arc cosine of positive and negative decimals
print("acos(0.55): ", math.acos(0.55))
print("acos(-0.55):", math.acos(-0.55))
# Calculate the arc cosine of 0 (corresponds to pi/2)
print("acos(0): ", math.acos(0))
# Calculate the arc cosine of boundary values (-1 and 1)
print("acos(1): ", math.acos(1)) # Corresponds to 0.0
print("acos(-1): ", math.acos(-1)) # Corresponds to pi
```
**Output:**
```text
acos(0.55): 0.9884320889261531
acos(-0.55): 2.15316056466364
acos(0): 1.5707963267948966
acos(1): 0.0
acos(-1): 3.141592653589793
```
---
### Considerations & Exceptions
When working with `math.acos()`, keep the following rules in mind to avoid runtime errors:
#### 1. Value Error (Out of Range)
The input parameter `x` must strictly be in the range $[-1, 1]$. If `x` is outside this range, Python will raise a `ValueError`.
```python
import math
# This will raise a ValueError: math domain error
try:
math.acos(1.5)
except ValueError as e:
print("Error:", e)
```
**Output:**
```text
Error: math domain error
```
#### 2. Type Error
The input parameter `x` must be a number. If you pass a string, list, or any other non-numeric type, Python will raise a `TypeError`.
```python
import math
# This will raise a TypeError
try:
math.acos("0.5")
except TypeError as e:
print("Error:", e)
```
**Output:**
```text
Error: must be real number, not str
```
#### 3. Converting Radians to Degrees
Because `math.acos()` returns the result in **radians**, you might want to convert it to **degrees** for certain applications. You can easily achieve this using `math.degrees()`:
```python
import math
radians_val = math.acos(0.5)
degrees_val = math.degrees(radians_val)
print(f"Radians: {radians_val}")
print(f"Degrees: {degrees_val}°")
```
**Output:**
```text
Radians: 1.0471975511965979
Degrees: 59.99999999999999°
```