Trigonometry

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Forms of Trigonometry

Trigonometry can be calculated in two forms;

- Degrees

- Radians

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What are Degrees and Radians

Degrees is an accepted unit of plane angles although, they are a fairly innaccurate representation of actual angles. Degrees are in the form of 1/360 meaning tthat there are 360 degrees in a full circle.

Radians are a more accurate representation of angles than Degrees and are therefore used in the International System of Units. radians come in the form of 2π

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Trigonomic Functions

Trigonometry has six different functions you will have to understand;

- Sin(x)

- Cos(x)

- Tan(x) = Sin(x)/Cos(x)

- Cosec(x) = 1/Sin(x)

- Sec(x) = 1/Cos(x)

- Cot(x) = 1/Tan(x) = Cos(x)/Sin(x)

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Trigonomety: Identities 1

There are many trigonomic identities but most of them can be found from the 4 main ones;

- Sin(A ± B) = Sin(A) Cos(B) ± Sin(B) Cos(A)

- Cos(A ± B) = Cos(A) Cos(B) Sin(A) Sin(B)

- Tan (A ± B) = (Tan(A) ± Tan(B))/(1 Tan(A) Tan(B))

- Sin² + Cos² = 1

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Trigonomety: Identities 2

You can find other equations from the first four, for example;

- Sin(A ± B) = Sin(A) Cos(B) ± Sin(B) Cos(A)

  Sin(A + A) = Sin(A) Cos(A) + Sin(A) Cos(A)

       Sin(2A) = 2 Sin(A) Cos (A)


-                   Sin² + Cos² = 1

  Sin²/Cos² + Cos²/Cos² = 1/Cos²

                          Tan² + 1 = Sec²

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Trigonometry: Differentiation

When differentiating Sin(x), you get a different trigonomic function. Which, if differentiated again, turns into the negative of Sin(x).

-        y = Sin(x)

  Dy/Dx = Cos(x)

-        y = Cos(x)

  Dy/Dx = - Sin(x)

-        y = - Sin(x)

  Dy/Dx = - Cos(x)

-        y = - Cos(x)

  Dy/Dx = Sin(x)

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Trigonometry: Integration

When integrating a trigonomic function, the opposite of the differentiation happens.

- Dy/Dx = Sin(x)

         y = - Cos(x) 

- Dy/Dx = - Cos(x)

         y = - Sin(x) 

- Dy/Dx = - Sin(x)

         y = Cos(x)

 

- Dy/Dx = Cos(x)

         y = Sin(x)

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Differentiation and Integration Circle

                                     (http://aerostudents.com/files/calculus/trigonometricCircle.jpg)

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