Trigonometry Basics: Sine, Cosine, and Tangent Explained

Trigonometry is the study of how the angles and sides of triangles relate to each other. The three main ratios — sine, cosine, and tangent — give you a way to calculate unknown sides or angles in any right triangle. These relationships are foundational across engineering, physics, architecture, and computer graphics.

SOH-CAH-TOA: the memory trick

Sine = Opposite / Hypotenuse. Cosine = Adjacent / Hypotenuse. Tangent = Opposite / Adjacent. In a right triangle, pick an angle (not the right angle). "Opposite" is the side across from it; "adjacent" is the side next to it; "hypotenuse" is always the longest side, opposite the right angle. SOH-CAH-TOA encodes all three ratios.

Using trig to find missing sides

If you know one angle and one side, you can find any other side. Example: a ladder leans against a wall at a 70° angle with the ground, and the base is 2 meters from the wall. The ladder length (hypotenuse) is 2 / cos(70°) ≈ 5.85 meters. The trigonometry calculator handles any such problem.

Inverse trig: finding angles

If you know two sides but need the angle, use the inverse functions: arcsin, arccos, arctan (also written sin⁻¹, cos⁻¹, tan⁻¹). If a ramp rises 1 meter over a horizontal distance of 4 meters, the angle is arctan(1/4) ≈ 14°. These are built into the calculator along with degree/radian conversion.