Fundamental Mathematics/Trigonometry

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Angles[edit]

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When two lines AB and AC cuts at one point A , angle is formed at point A between AB and AC . Angle is denoted as . Angle is measured in Degree (o) or Radian (Rad) .

To convert degrees to radians:

To convert radians to degrees:

Trigonometric functions[edit]

Fundamental trigonometric functions[edit]

Relation of right triangle sides are defined as trigonometric functions. They are:

Trignometric Function Definition Mathematical Formula Graphs
Sine Ratio of opposite side over hypotnuse Sin.svg
Cosine Ratio of adjacent side over hypotnuse Cos.svg
Tangent Ratio of opposite over Adjacent Tan.svg
Co tangent Ratio of adjacent over opposite Cot.svg
Secant Ratio of 1 over opposite Sec.svg
Co secant Ratio of 1 over adjacent Csc.svg

Chracteristics[edit]

Periodic

Symmetry


Phase shift


Complex Power


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de Moivre's formula:
Limit

Derivative

Trigonometric formulas[edit]

Fundamental trigonometry function[edit]

Sum and difference angles[edit]

Reduced power[edit]

Half angles[edit]

      and     and  

Product of trigonomtric functions[edit]

Inverse trigonometric functions[edit]

Complex number[edit]

With

Hence

Infinite Product[edit]

Limits[edit]

Derivatives[edit]

Common Trigonomtric functions[edit]

Double angle trigonometric functions[edit]

In general,

If Tn is Chebyshev n ordered then

De Moivre formula:

hạt nhân Dirichlet Dn(x) sẽ xuất hiện trong các công thức sau:

Triple angle trigonometric functions[edit]

Series[edit]

Integrals[edit]

Complex trigonometric functions[edit]

Further reading[edit]