YouTipRef Math Cos
## Python math.cos() Method
The `math.cos()` method is a built-in function in Python's standard `math` module. It returns the cosine of a given angle expressed in radians.
---
### Introduction
In trigonometry, the cosine of an angle in a right-angled triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. The `math.cos(x)` method calculates this value for an angle `x` (in radians).
* **Python Version Added:** 1.4
* **Domain:** $[-1.0, 1.0]$ (The returned float value will always be between -1 and 1, inclusive).
---
### Syntax
To use the `math.cos()` method, you must first import the `math` module:
```python
import math
math.cos(x)
```
#### Parameters
| Parameter | Type | Description |
| :--- | :--- | :--- |
| **x** | `float` or `int` | **Required.** A numeric value representing the angle in **radians**. |
#### Return Value
* **Type:** `float`
* **Description:** Returns a floating-point value between `-1.0` and `1.0` representing the cosine of the angle `x`.
#### Exceptions
* If `x` is not a number (e.g., a string or a list), the method raises a `TypeError`.
---
### Code Examples
#### Basic Usage
The following example demonstrates how to calculate the cosine of various values:
```python
import math
# Calculate cosine for different values
print(math.cos(0.00)) # Cosine of 0
print(math.cos(-1.23)) # Cosine of a negative number
print(math.cos(10)) # Cosine of an integer
print(math.cos(3.14159265359)) # Cosine of Pi (approximate)
```
**Output:**
```text
1.0
0.3342377271245026
-0.8390715290764524
-1.0
```
---
### Considerations & Common Workflows
#### 1. Converting Degrees to Radians
Because `math.cos()` expects the input angle to be in **radians**, passing degrees directly will yield incorrect results. You must convert degrees to radians first using either:
* `math.radians(degrees)`
* The mathematical formula: $\text{radians} = \text{degrees} \times \frac{\pi}{180}$
```python
import math
degrees = 60
# Method 1: Using math.radians()
radians_1 = math.radians(degrees)
print(f"Cosine of 60 degrees: {math.cos(radians_1)}") # Expected: ~0.5
# Method 2: Manual conversion using math.pi
radians_2 = degrees * (math.pi / 180)
print(f"Cosine of 60 degrees (manual): {math.cos(radians_2)}")
```
**Output:**
```text
Cosine of 60 degrees: 0.5000000000000001
Cosine of 60 degrees (manual): 0.5000000000000001
```
*(Note: Due to floating-point precision limitations, the output may be extremely close to `0.5` rather than exactly `0.5`.)*
#### 2. Handling Type Errors
If you pass a non-numeric value to the function, Python will raise a `TypeError`:
```python
import math
try:
math.cos("90")
except TypeError as e:
print(f"Error: {e}")
```
**Output:**
```text
Error: must be real number, not str
```