degrees to radians conversion

How to convert degrees to radians?

Sure, I'd be happy to explain how to convert degrees to radians and provide some real-world examples!

Converting Degrees to Radians

The unit circle is commonly used to convert between degrees and radians. The full circle is $360^\circ$ or $2\pi$ radians. To convert degrees to radians, you can use the following formula:

$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$

So to convert $1^\circ$ to radians:

$1^\circ \times \frac{\pi}{180} = \frac{\pi}{180} \approx 0.0174533 \text{ radians}$

Real-World Examples

1. 90 Degrees: This is a right angle, commonly seen in many everyday contexts such as the corners of a square or rectangle. $90^\circ \times \frac{\pi}{180} = \frac{\pi}{2} \text{ radians} \approx 1.5708 \text{ radians}$

2. 180 Degrees: This represents a straight line or half a full turn. $180^\circ \times \frac{\pi}{180} = \pi \text{ radians} \approx 3.1416 \text{ radians}$

3. 45 Degrees: This is often used in right triangles and is the angle of inclination in many architectural designs. $45^\circ \times \frac{\pi}{180} = \frac{\pi}{4} \text{ radians} \approx 0.7854 \text{ radians}$

4. 360 Degrees: This represents a full circle or a complete turn. $360^\circ \times \frac{\pi}{180} = 2\pi \text{ radians} \approx 6.2832 \text{ radians}$

By understanding how to convert degrees to radians, you can work seamlessly between these units in various applications, whether in mathematics, physics, engineering, or everyday problem-solving.