Trigonométrie (1_11)
5.2 Lignes trigonométriques
5.2.1 Propriétés
x | 0 | π | π | π | π | ||||
6 | 4 | 3 | 2 | ||||||
---|---|---|---|---|---|---|---|---|---|
sinx | 0 | 1 | √2 | √3 | 1 | ||||
2 | 2 | 2 | |||||||
cosx | 1 | √3 | √2 | 1 | 0 | ||||
2 | 2 | 2 | |||||||
tanx | 0 | √3 | 1 | √3 | × | ||||
3 |
5.3- Relations entre les lignes trigonométriques
5.3.1 Propriétés
cos(-x) = cosx | sin(-x) = -sinx | |
sin(x+2kπ) = sinx | cos(x+2kπ) = - cosx | tan(-x) = - tanx | tan(x+kπ) = tanx |
sin(π-x) = sinx | cos(π-x)= - cosx | |
sin(π+x) = - sinx | cos(π+x)= - cosx | |
tan(π-x) =- tanx | tan(π+x)= tanx |
sin( | π | - x) = cosx | |
2 | |||
cos( | π | - x) = sinx | |
2 | |||
sin( | π | + x) = cosx | |
2 | |||
cos( | π | + x) = - sinx | |
2 |
tan( | π | - x) = | 1 | |
2 | tanx | |||
tan( | π | + x)=- | 1 | |
2 | tanx |
Exercice 1 tp
Simplifier ce qui suit
A=cos(4π+x)+cos(3π-x).
B=sin(9π-x)+sin(x+8π).
C=tan(3π-x)+tan(4π+x).
Correction
A=cos(x+2.2π)+cos(π+2.1π-x).
A=cosx+cos(π-x)=cosx-cosx donc A=0
B=sin(π+2.4π-x)+sin(x+2.4π).
B=sin(π-x)+sin(x)=sinx+sinx
donc B=2sinx.
C=tan(-x+3π)+tan(x+4π).
=tan(-x)+tan(x)=- tanx+tanx=0
donc C=0.
Exercice 2 tp
Calculer
cos( | 7π | ) ; sin( | 13π | ) |
4 | 3 | |||
tan( | -83π | ) ; tan( | 2021π | ) |
4 | 3 |