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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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