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Basic definition of the trigonometric functions
Cosine function

Particular values of the cosine function (cos):

    \(\displaystyle cos(0^{\circ})=cos(0)=1\)

    \(\displaystyle cos(30^{\circ})=cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2}\)

    \(\displaystyle cos(45^{\circ})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\)

    \(\displaystyle cos(60^{\circ})=cos(\frac{\pi}{3})=\frac{1}{2}\)

    \(\displaystyle cos(90^{\circ})=cos(\frac{\pi}{2})=0\)

    \(\displaystyle cos(x + 2\pi)=cos(x)\)


Sine function

Particular values of the sine function (sin):

    \(\displaystyle sin(0^{\circ})=sin(0)=0\)

    \(\displaystyle sin(30^{\circ})=sin(\frac{\pi}{6})=\frac{1}{2}\)

    \(\displaystyle sin(45^{\circ})=sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\)

    \(\displaystyle sin(60^{\circ})=sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\)

    \(\displaystyle sin(90^{\circ})=sin(\frac{\pi}{2})=1\)

    \(\displaystyle sin(x + 2\pi)=sin(x)\)


Tangent function

Particular values of the tangent function (tan):

    \(\displaystyle tan(0^{\circ})=tan(0)=0\)

    \(\displaystyle tan(30^{\circ})=tan(\frac{\pi}{6})=\frac{\sqrt{3}}{3}\)

    \(\displaystyle tan(45^{\circ})=tan(\frac{\pi}{4})=1\)

    \(\displaystyle tan(60^{\circ})=tan(\frac{\pi}{3})=\sqrt{3}\)

    The tangent function is not defined at \(\displaystyle \frac{\pi}{2}\) (\(\displaystyle 90^{\circ}\)).

    \(\displaystyle tan(x + \pi)=tan(x)\)


Relationships between trigonometric functions

Main relationships between trigonometric functions:

    \(\displaystyle cos^2(x)+sin^2(x)=1\)

    \(\displaystyle tan(x)=\frac{sin(x)}{cos(x)}\)

    \(\displaystyle \frac{1}{cos^2(x)}=1+tan^2(x)\)

    \(\displaystyle cotan(x)=\frac{1}{tan(x)}\)

    \(\displaystyle cotan(x)=\frac{cos(x)}{sin(x)}\)

    \(\displaystyle \frac{1}{sin^2(x)}=1+cotan^2(x)\)
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