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# Circular funcions

### Formula

Theorems/PropertiesFormulas/Definitions
Cosine. cos(u) = x. domain: |R. range: [-1, 1]. period: 2*pi.
Sine. sin(u) = y. domain: |R. range: [-1, 1]. period: 2*pi.
Secant. sec(u) = 1/x. domain: u not = {pi/2 + k*pi}. range: (-@, -1]U[1,@). period: 2*pi.
Cosecant. csc(u) = 1/y. domain: u not = {pi*k}. range: (-@,-1]U[1,@). period: 2*pi.
Tangent. tan(u) = y/x. domain: u not = {pi/2 + k*pi}. range: |R. period: pi.
Cotangent. cot(u) = x/y. domain: u not = {k*pi} range: |R. period: pi.
Reference angle theorem. Let's i be the reference angle of u. sec(u) = -/+ sec(i), csc(u) = -/+ csc(i), tan(u) = -/+ tan(i), cot(u) = -/+ cot(i).
Pythagorean identities. sec²(u) - tan²(u) = 1. csc²(u) - cot²(u) = 1.
Beyond unit circle. L(x,y) and r= sqrt(x² + y²). sec(u) = r/x and csc(u) = r/y.
Trigonometric functions features. A: amplitude. period: (2*pi)/(omega). phase shift: - (phi)/(omega). phase: phi. vertical shift: B
Periodicity. The period of a function is the smallest value p such as: f(x + p) = f(x).
Created by: JuniorDBlackbone