Mathematics — Functions

[Definition of a function]

, x: independent variable, y: there is one-to-one correspondence between x and y. For a given x, there should be only one value of y (single-valuedness). f(x) is a rule specifying how y is corresponded with x. f(x) is called a function of x.

[Trigonometric function]

(right triangle)

cofunction:

Radian and degree: Exactly one rotation around a circle → 2π radian = 360 degrees → 1 radian = 360/(2 π) = 57.3 degrees; 1 degree = 17.5 milliradian

Trigonometric functino at special angles:

Trigonometric identities:

(Pythagorean identities)

(even-odd identities)

(sum formulas)

(double angle formulas)

(half-angle formulas)

(product-to-sum formula)

(sum-to-product formula)

cofunction:

Quadrant sign rule