Trigonometric Unit Circle Simulator

Adjust Angle θ

Sine

$$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$$

0.7071

Cosine

$$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$$

0.7071

Tangent

$$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$$

1.0000

📐 Understanding Trig Ratios & Signs on the Unit Circle

On the unit circle (radius of 1), the coordinates of a point $(x, y)$ on the circumference directly represent $(\cos\theta, \sin\theta)$. Additionally, the line tangent to the circle intersecting the $x$-axis corresponds to $\tan\theta$. Observe how each ratio's sign (positive/negative) changes as the angle increases from Quadrant I to Quadrant IV.