 Curiosity, learning and homework help

:

### MEMBERS

 Come to discuss on the forum!■ FAST and FREE signup. ■ 😀 Access to discussion forums 😀 Help for HOMEWORKS, support in COMPUTER SCIENCE, help for learning FRENCH and ENGLISH, discussion on your INTERESTS and HOBBIES...

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:

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

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

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

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

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

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