Circular Functions Definitions
n ∈ ℕ1 = {1,2,3,4,5,...} |
Hyperbolic Functions Definitions
n ∈ ℕ1 = {1,2,3,4,5,...} |
Complex Definitions
i=√(-1) z is a complex variable of the form a+bi, where a and b are real numbers, and i is the imaginary number |
Circular Functions Unit Circle Values
The coordinates (cos(θ),sin(θ)) represent x and y coordinates of θ on the unit circle x2+y2=1 |
Circular-Inverse Compositional Identities
Each composition is valid on different domains |
Circular Quotient & Reciprocal Identities
All the following identities are true for values that do not cause division by zero Cofunctional Phase Shift Properties
n ∈ ℕ1 = {1,2,3,4,5,...} Periodicity Properties
n ∈ ℕ1 = {1,2,3,4,5,...} Circular Parity Properties
Circular Pythagorean Identities
The last two triplets of Pythagorean Identities are obtained by dividing all the terms of the original Sine-Cosine Identity by sin²(θ) or cos²(θ) (C) Half/Multiple-Angle Identities
Sine Multiple-Angle Formula: sin(nθ)=∑nk=0 (nk)cosk(θ)sinn-k(θ)sin((π/2)(n-k)) Cosine Multiple-Angle Formula: cos(nθ)=∑nk=0 (nk)cosk(θ)sinn-k(θ)cos((π/2)(n-k)) Circular Sum/Difference/Product Identities
Law of Sines/Cosines/Tangents
Side lengths a, b, and c are opposite of the angles α, β, and γ, respectively. Measurements And Formulas
Radians are unitless a, b, and c are side lengths of a right-triangle Sine and Cosine Unit CircleTangent Unit CircleRight-Triangle Relations |
Circular-Inverse Reciprocal Identities
Circular-Inverse Complimentary Identities
Circular-Inverse Negative Input Identities
(CI) Half/Multiple Substitution Identities
Each identity is valid for the proper domains of the functions Circular-Inverse Sum/Difference Identities
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(H) Quotient & Reciprocal Identities
All the following identities are true for values that do not cause division by zero Hyperbolic Parity Properties
(HI) Negative Input Identities
Hyperbolic Pythagorean Identities
The last two triplets of Hyperbolic Pythagorean Identities are obtained by dividing all the terms of the original Sine-Cosine Identity by sinh²(θ) or cosh²(θ) (H) Half-Angle & Multiple-Angle Identities
(H) Sum/Difference/Product Identities
Unit Hyperbola |