What is a Degree? 🍕

Imagine slicing a pizza 🍕 into 360 equal pieces. Each tiny slice represents 1 degree (1°). Degrees are the most common way we talk about angles in everyday life.

Examples:

• A right angle (like a square corner) is 90°.
• A straight line is 180°.
• A full circle is 360° (the whole pizza!).

What are Minutes and Seconds? ⏱

Sometimes degrees need to be more precise! For that, we break them down further:

• 1 degree = 60 minutes (60′)
• 1 minute = 60 seconds (60″)

Think of it like time on a clock. An angle like 90° 30′ 15″ means 90 degrees, 30 minutes, and 15 seconds.

What is a Radian? 🎡

Radians are another way to measure angles, often preferred in mathematics and physics because they simplify many formulas. Here's the idea:

1. Take the radius of a circle (distance from center to edge).
2. Lay that length along the circle's edge.
3. The angle formed from the center to the ends of that arc is 1 radian.

Key Radian Facts:

• A full circle (360°) is 2π radians (about 6.28 rad).
• Half a circle (180°) is π radians (about 3.14 rad).
• A right angle (90°) is π/2 radians (about 1.57 rad).

Quick Conversion: Degrees ↔ Radians 🧮

The key relationship is: 180° = π radians. Use this to convert:

• Radians = Degrees × (π / 180)
• Degrees = Radians × (180 / π)

Why Use Radians?

Radians are the 'natural' unit for angles in higher math and science, making calculus and physics equations cleaner. While degrees are great for everyday use, radians are essential for technical fields.