Sine Wave & Unit Circle Explorer

What is the Unit Circle?

The unit circle is a circle with radius 1 centred at the origin (0, 0). Any point on the circle can be described by an angle θ (theta) measured counter-clockwise from the positive x-axis.

The sine of the angle is simply the y-coordinate of the point on the circle. It oscillates between −1 and +1 as the angle goes from 0° to 360°.

The Sine Function

• 0° → 90°: sin goes from 0 up to 1
• 90° → 180°: sin goes from 1 back to 0
• 180° → 270°: sin goes from 0 down to −1
• 270° → 360°: sin goes from −1 back to 0

Key Angles to Remember

• 0° / 360° — sin = 0  (rightmost point)
• 90° — sin = +1  (top of circle)
• 180° — sin = 0  (leftmost point)
• 270° — sin = −1  (bottom of circle)

The sine wave completes one full cycle every 360° (or 2π radians).

Why Does This Matter?

Sine waves appear everywhere in nature and technology: sound waves, light, alternating electrical current, heartbeats, tides, and springs. Understanding the unit circle is the foundation for trigonometry, signal processing, and physics.