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Populaire Trigonométrie >

(sin(55.01-x))/(sin(x))= 1200/500

Solution

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Solution

x = 2.75168 \dots + πn

Degrés

x = 157.65972 \dots^{\circ} + 18 0^{\circ} n

étapes des solutions

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Récrire en utilisant des identités trigonométriques

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Récrire en utilisant des identités trigonométriques

sin (55.01 - x)

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

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

= sin (55.01) cos (x) - cos (55.01) sin (x)

Simplifier

sin (55.01) cos (x) - cos (55.01) sin (x) : - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

sin (55.01) cos (x) - cos (55.01) sin (x)

Simplifier

sin (55.01) : - 0.99948 \dots

sin (55.01)

sin (55.01) = - 0.99948 \dots

= - 0.99948 \dots

= - 0.99948 \dots cos (x) - cos (55.01) sin (x)

Simplifier

cos (55.01) : 0.03212 \dots

cos (55.01)

cos (55.01) = 0.03212 \dots

= 0.03212 \dots

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{1200}{500}

\frac{1200}{500} = \frac{12}{5}

\frac{1200}{500}

Annuler le facteur commun :

100

= \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

Soustraire

\frac{12}{5}

des deux côtés

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} - 2.4 = 0

Récrire en utilisant des identités trigonométriques

- 2.4 + \frac{- 0.03212 \dots sin ( x ) - 0.99948 \dots cos ( x )}{sin ( x )}

Utiliser l'identité trigonométrique de base:

sin (x) = \frac{1}{csc ( x )}

= - 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

Simplifier

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}} : - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}} = csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

Appliquer la règle des fractions:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{( - 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x ) ) csc ( x )}{1}

0.03212 \dots \cdot \frac{1}{csc ( x )} = \frac{0.03212 \dots}{csc ( x )}

0.03212 \dots \cdot \frac{1}{csc ( x )}

Multiplier des fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 0.03212 \dots}{csc ( x )}

Multiplier les nombres :

1 \cdot 0.03212 \dots = 0.03212 \dots

= \frac{0.03212 \dots}{csc ( x )}

= \frac{csc ( x ) ( - \frac{0.03212 \dots}{c s c ( x )} - 0.99948 \dots cos ( x ) )}{1}

Appliquer la règle des fractions:

\frac{a}{1} = a

= (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x)) csc (x)

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

Développer

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x)) : - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

Appliquer la loi de la distribution:

a (b - c) = ab - a c

a = csc (x), b = - \frac{0.03212 \dots}{csc ( x )}, c = 0.99948 \dots cos (x)

= csc (x) (- \frac{0.03212 \dots}{csc ( x )}) - csc (x) \cdot 0.99948 \dots cos (x)

Appliquer les règles des moins et des plus

+ (- a) = - a

= - \frac{0.03212 \dots}{csc ( x )} csc (x) - 0.99948 \dots csc (x) cos (x)

\frac{0.03212 \dots}{csc ( x )} csc (x) = 0.03212 \dots

\frac{0.03212 \dots}{csc ( x )} csc (x)

Multiplier des fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{0.03212 \dots csc ( x )}{csc ( x )}

Annuler le facteur commun :

csc (x)

= 0.03212 \dots

= - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

= - 2.4 - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

Soustraire les nombres :

- 2.4 - 0.03212 \dots = - 2.43212 \dots

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

csc (x) cos (x) = cot (x)

csc (x) cos (x)

Exprimer avec sinus, cosinus

csc (x) cos (x)

Utiliser l'identité trigonométrique de base:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} cos (x)

Simplifier

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

Multiplier des fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 cos ( x )}{sin ( x )}

Multiplier:

1 \cdot cos (x) = cos (x)

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

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

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

Utiliser l'identité trigonométrique de base:

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

= cot (x)

= - 2.43212 \dots - 0.99948 \dots cot (x)

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

Déplacer

2.43212 \dots

vers la droite

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

Ajouter

2.43212 \dots

aux deux côtés

- 2.43212 \dots - 0.99948 \dots cot (x) + 2.43212 \dots = 0 + 2.43212 \dots

Simplifier

- 0.99948 \dots cot (x) = 2.43212 \dots

- 0.99948 \dots cot (x) = 2.43212 \dots

Diviser les deux côtés par

- 0.99948 \dots

- 0.99948 \dots cot (x) = 2.43212 \dots

Diviser les deux côtés par

- 0.99948 \dots

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

Simplifier

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

Simplifier

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} : cot (x)

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots}

Appliquer la règle des fractions:

\frac{- a}{- b} = \frac{a}{b}

= \frac{0.99948 \dots cot ( x )}{0.99948 \dots}

Annuler le facteur commun :

0.99948 \dots

= cot (x)

Simplifier

\frac{2.43212 \dots}{- 0.99948 \dots} : - 2.43337 \dots

\frac{2.43212 \dots}{- 0.99948 \dots}

Appliquer la règle des fractions:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2.43212 \dots}{0.99948 \dots}

Diviser les nombres :

\frac{2.43212 \dots}{0.99948 \dots} = 2.43337 \dots

= - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

Appliquer les propriétés trigonométriques inverses

cot (x) = - 2.43337 \dots

Solutions générales pour

cot (x) = - 2.43337 \dots

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- 2.43337 \dots) + πn

x = arccot (- 2.43337 \dots) + πn

Montrer les solutions sous la forme décimale

x = 2.75168 \dots + πn

Graphe

Exemples populaires

csc(θ)=0.77

csc (θ) = 0.77

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