Sine and cosine on the unit circle

Imagine a circle with radius one, and a spinning arm inside it.

The unit circle is a circle with radius exactly one, centered at the origin. When the arm rotates to an angle, it touches the circle at a point. The x-coordinate of that point is the cosine of the angle.

• Radius = 1
• Angle = 45 degrees

The y-coordinate of that point is the sine of the angle. At zero degrees, the arm points right: cosine is one, sine is zero.

At ninety degrees, the arm points up: cosine is zero, sine is one.

At forty-five degrees, both are equal: about zero point seven.

At one hundred eighty degrees, the arm points left: cosine is minus one.

Here's the key: sine and cosine are just the coordinates of a point on the unit circle.

Quick quiz: at sixty degrees, which is bigger, sine or cosine? Sine and cosine are the secret bridge between angles and coordinates.

• sin = y-coordinate, cos = x-coordinate