Trigonometry Essentials
Trigonometry studies the relationships between angles and sides in triangles. For a right triangle, three ratios do all the work: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse,tan θ = opposite/adjacent — remembered with the mnemonic SOH-CAH-TOA.
The Unit Circle
On a circle of radius 1, the coordinates of any angle are simply (cos θ, sin θ). The exact values at 30°, 45°, 60°, and 90° come from splitting equilateral triangles and squares — memorize those four and you can derive the rest with symmetry. The table above lists every standard angle.
Degrees vs. Radians
Radians measure angles by arc length: a full circle is 2π radians. Convert with radians = degrees × π/180. Calculus (derivatives of sin and cos, Taylor series) only works cleanly in radians — see our derivative calculator.