Triangles, angles, and the unit circle
Trigonometry connects angles to side lengths in triangles. It is essential for physics, engineering, navigation, and computer graphics. The three basic ratios — sine, cosine, and tangent — are the foundation of all trigonometry.
In a right triangle: sin = Opposite/Hypotenuse, cos = Adjacent/Hypotenuse, tan = Opposite/Adjacent. This mnemonic is the key to all basic trig.
A circle of radius 1 centered at the origin. The x-coordinate of a point on the circle is cos(θ), and the y-coordinate is sin(θ). This extends trig to any angle.
sin²θ + cos²θ = 1. This is always true and is the basis for many other trig identities.
a/sin(A) = b/sin(B) = c/sin(C). Used for non-right triangles when you know two angles and a side.
c² = a² + b² − 2ab·cos(C). Generalizes the Pythagorean theorem to any triangle.
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