Sine, Cosine, and Tangent Using Ratios of Sides of a Right-Angled Triangle

This Demonstration shows a right-angled triangle, its side lengths, and the basic trigonometric functions as ratios of the sides lengths. You can change the angle or the scale to get similar triangles. The functions do not change when the triangle is scaled because the side lengths change by the same factor and so cancel in the ratios. The thumbnail shows the familiar 3-4-5 triangle.