Exercice 1 tp

Calculer

a = cos(	23π	+15π)
	4
b = sin(5π-	3π	)
	4

Correction

a = cos(	23π	+15π) = cos(π-	3π	)
	4		4

Donc a = -cos	3π	= -	√(2)
	4		2

b = sin( 5π -	3π	)
	4
= sin(π-	3π	)
	4

donc b = sin	3π	=	√(2)
	4		2

Exercice 2 tp

Calculer

cos²(	7π	+15π) + sin²(3π-	3π	)
	5		5

Exercice 3 tp

Calculer

a = cos(	27π	+	π	)
	2		3

Correction

a = cos(	27π	+	π	)
	2		3
= cos(	28π-π	+	π	)
	2		3

ou encore

= cos(	-π	+ 14π +	π	)
	2		3
= cos(	-π	+	π	)
	2		3
= cos(	π	-	π	)
	2		3

donc a = sin	π	=	1
	3		2

Exercice 4 tp

Calculer

a = sin(	5π	-	π	)
	2		4
b = cos(	5π	+	π	)
	2		3

Correction

a = sin(	5π	-	π	)
	2		4
= sin(	4π+π	-	π	)
	2		4

ou encore

a = sin(	π	+ 2π -	π	)
	2		4
= sin(	π	-	π	)
	2		4

donc, a = cos	π	=	√(2)
	4		2

b = cos(	5π	+	π	)
	2		3

Ou encore

b = cos(	4π+π	+	π	)
	2		3
= cos(	π	+ 2π +	π	)
	2		3
= cos(	π	+	π	)
	2		3

donc b = -sin	π	=	- √(3)
	3		2