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Populaire Trigonométrie >

4sin(2x-0.4)-5cos(2x-0.4)=0

Solution

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

Solution

x = \frac{1.29605 \dots}{2} + \frac{πn}{2}

Degrés

x = 37.12925 \dots^{\circ} + 9 0^{\circ} n

étapes des solutions

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

Récrire en utilisant des identités trigonométriques

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

Récrire en utilisant des identités trigonométriques

sin (2 x - 0.4)

Utiliser l'identité de la différence de l'angle :

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (2 x) cos (0.4) - cos (2 x) sin (0.4)

Simplifier

sin (2 x) cos (0.4) - cos (2 x) sin (0.4) : 0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

sin (2 x) cos (0.4) - cos (2 x) sin (0.4)

Simplifier

cos (0.4) : 0.92106 \dots

cos (0.4)

cos (0.4) = 0.92106 \dots

= 0.92106 \dots

= 0.92106 \dots sin (2 x) - sin (0.4) cos (2 x)

Simplifier

sin (0.4) : 0.38941 \dots

sin (0.4)

sin (0.4) = 0.38941 \dots

= 0.38941 \dots

= 0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

= 0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

Utiliser l'identité de la différence de l'angle :

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (2 x) cos (0.4) + sin (2 x) sin (0.4)

Simplifier

cos (2 x) cos (0.4) + sin (2 x) sin (0.4) : 0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

cos (2 x) cos (0.4) + sin (2 x) sin (0.4)

Simplifier

cos (0.4) : 0.92106 \dots

cos (0.4)

cos (0.4) = 0.92106 \dots

= 0.92106 \dots

= 0.92106 \dots cos (2 x) + sin (0.4) sin (2 x)

Simplifier

sin (0.4) : 0.38941 \dots

sin (0.4)

sin (0.4) = 0.38941 \dots

= 0.38941 \dots

= 0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

= 0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)) = 0

Simplifier

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)) : 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

Développer

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) : 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x))

Appliquer la loi de la distribution:

a (b - c) = ab - a c

a = 4, b = 0.92106 \dots sin (2 x), c = 0.38941 \dots cos (2 x)

= 4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

Simplifier

4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x) : 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

Multiplier les nombres :

4 \cdot 0.92106 \dots = 3.68424 \dots

= 3.68424 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

Multiplier les nombres :

4 \cdot 0.38941 \dots = 1.55767 \dots

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

Développer

- 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)) : - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

- 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

Appliquer la loi de la distribution:

a (b + c) = ab + a c

a = - 5, b = 0.92106 \dots cos (2 x), c = 0.38941 \dots sin (2 x)

= - 5 \cdot 0.92106 \dots cos (2 x) + (- 5) \cdot 0.38941 \dots sin (2 x)

Appliquer les règles des moins et des plus

+ (- a) = - a

= - 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

Simplifier

- 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x) : - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

- 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

Multiplier les nombres :

5 \cdot 0.92106 \dots = 4.60530 \dots

= - 4.60530 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

Multiplier les nombres :

5 \cdot 0.38941 \dots = 1.94709 \dots

= - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

= - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

Simplifier

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x) : 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

Additionner les éléments similaires :

- 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) = - 6.16297 \dots cos (2 x)

= 3.68424 \dots sin (2 x) - 6.16297 \dots cos (2 x) - 1.94709 \dots sin (2 x)

Additionner les éléments similaires :

3.68424 \dots sin (2 x) - 1.94709 \dots sin (2 x) = 1.73715 \dots sin (2 x)

= 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

= 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x) = 0

Diviser les deux côtés par

cos (2 x), cos (2 x) \neq = 0

\frac{1.73715 \dots sin ( 2 x ) - 6.16297 \dots cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplifier

\frac{1.73715 \dots sin ( 2 x )}{cos ( 2 x )} - 6.16297 \dots = 0

Utiliser l'identité trigonométrique de base:

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

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

Déplacer

6.16297 \dots

vers la droite

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

Ajouter

6.16297 \dots

aux deux côtés

1.73715 \dots tan (2 x) - 6.16297 \dots + 6.16297 \dots = 0 + 6.16297 \dots

Simplifier

1.73715 \dots tan (2 x) = 6.16297 \dots

1.73715 \dots tan (2 x) = 6.16297 \dots

Diviser les deux côtés par

1.73715 \dots

1.73715 \dots tan (2 x) = 6.16297 \dots

Diviser les deux côtés par

1.73715 \dots

\frac{1.73715 \dots tan ( 2 x )}{1.73715 \dots} = \frac{6.16297 \dots}{1.73715 \dots}

Simplifier

tan (2 x) = 3.54774 \dots

tan (2 x) = 3.54774 \dots

Appliquer les propriétés trigonométriques inverses

tan (2 x) = 3.54774 \dots

Solutions générales pour

tan (2 x) = 3.54774 \dots

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x = arctan (3.54774 \dots) + πn

2 x = arctan (3.54774 \dots) + πn

Résoudre

2 x = arctan (3.54774 \dots) + πn : x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

2 x = arctan (3.54774 \dots) + πn

Diviser les deux côtés par

2

2 x = arctan (3.54774 \dots) + πn

Diviser les deux côtés par

2

\frac{2 x}{2} = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

Simplifier

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

Montrer les solutions sous la forme décimale

x = \frac{1.29605 \dots}{2} + \frac{πn}{2}

Graphe

Exemples populaires

cos(x)=-15/17

cos (x) = - \frac{15}{17}

sin(x)= 4/11

sin (x) = \frac{4}{11}

cos(x)=0.64

cos (x) = 0.64

solvefor x,cosh(sqrt(x))=0

so l v e f or x, cosh (x) = 0

cos(x)=0.57

cos (x) = 0.57