Trigonometric Equations

Solving sin(x) = 1/2 means finding every angle whose sine is 1/2. There are infinitely many: 30°, 150°, 390°, 510°, … The unit circle makes this visual — two points where the y-coordinate equals 1/2 — and the general solution captures all of them compactly. Double-angle and multiple-angle equations require using identities to reduce the equation before solving.