Trigonometry Explorer

The unit circle is a circle with a radius of exactly 1 centred at the origin. It is the foundation of trigonometry — every angle corresponds to a point on the circle whose coordinates are (cos θ, sin θ).

For any angle θ in a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent (which equals sin θ / cos θ).

Tangent is undefined at 90° and 270° because you would be dividing by cos(90°) = 0, and division by zero is impossible. On the unit circle, the tangent line becomes vertical at these angles.