TRIGONOMETRY
The study of the relationships between the side lengths and angles of triangles. Trigonometry allows us to calculate distances we cannot measure directly—like the height of a mountain or the distance to a star.
SOH CAH TOA
Every angle creates a specific ratio between the sides of a Right Triangle.
Sine (sin)
Vertical Component
Opposite / Hypotenuse
Cosine (cos)
Horizontal Component
Adjacent / Hypotenuse
Tangent (tan)
Slope (Rise / Run)
Opposite / Adjacent
The Secret Identity
Because these triangles live inside a circle with radius 1, the Pythagorean Theorem ($a^2 + b^2 = c^2$) becomes: sin²θ + cos²θ = 1
Unit Circle Explorer
Radius = 1
Angle (θ)45°
0.25π Radians
Sine (Height)
Opposite / 1
0.707
Cosine (Width)
Adjacent / 1
0.707
From Circle to Wave
Why do we use Sine waves for audio and light? Look at the background animation.
y
As you rotate around a circle (like a generator spinning), your vertical height ($y$) goes Up, Down, and back Up smoothly. This creates the Sine Wave.