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Populaire Trigonométrie >

129.8sin(a)-0.6129.8cos(a)=121.79

Solution

12 \cdot 9.8 \cdot sin (a) - 0.6 \cdot 12 \cdot 9.8 \cdot cos (a) = 12 \cdot 1.79

Solution

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

Degrés

a = - 158.04722 \dots^{\circ} + 36 0^{\circ} n, a = 39.97473 \dots^{\circ} + 36 0^{\circ} n

étapes des solutions

12 \cdot 9.8 sin (a) - 0.6 \cdot 12 \cdot 9.8 cos (a) = 12 \cdot 1.79

Ajouter

0.6129.8 cos (a)

aux deux côtés

117.6 sin (a) = 21.48 + 70.56 cos (a)

Mettre les deux côtés au carré

(117.6 sin (a))^{2} = (21.48 + 70.56 cos (a))^{2}

Soustraire

(21.48 + 70.56 cos (a))^{2}

des deux côtés

13829.76 sin^{2} (a) - 461.3904 - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) = 0

Récrire en utilisant des identités trigonométriques

- 461.3904 + 13829.76 sin^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

Utiliser l'identité hyperbolique:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= - 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

Simplifier

- 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) : - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

- 461.3904 + 13829.76 (1 - cos^{2} (a)) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

Développer

13829.76 (1 - cos^{2} (a)) : 13829.76 - 13829.76 cos^{2} (a)

13829.76 (1 - cos^{2} (a))

Appliquer la loi de la distribution:

a (b - c) = ab - a c

a = 13829.76, b = 1, c = cos^{2} (a)

= 13829.76 \cdot 1 - 13829.76 cos^{2} (a)

= 1 \cdot 13829.76 - 13829.76 cos^{2} (a)

Multiplier les nombres :

1 \cdot 13829.76 = 13829.76

= 13829.76 - 13829.76 cos^{2} (a)

= - 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

Simplifier

- 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) : - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

- 461.3904 + 13829.76 - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a)

Grouper comme termes

= - 13829.76 cos^{2} (a) - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) - 461.3904 + 13829.76

Additionner les éléments similaires :

- 13829.76 cos^{2} (a) - 4978.7136 cos^{2} (a) = - 18808.4736 cos^{2} (a)

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) - 461.3904 + 13829.76

Additionner/Soustraire les nombres :

- 461.3904 + 13829.76 = 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

= - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) + 13368.3696

13368.3696 - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) = 0

Résoudre par substitution

13368.3696 - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) = 0

Soit :

cos (a) = u

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0 : u = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, u = \frac{1014943029.424128 - 3031.2576}{37616.9472}

13368.3696 - 18808.4736 u^{2} - 3031.2576 u = 0

Ecrire sous la forme standard

a x^{2} + b x + c = 0

- 18808.4736 u^{2} - 3031.2576 u + 13368.3696 = 0

Résoudre par la formule quadratique

- 18808.4736 u^{2} - 3031.2576 u + 13368.3696 = 0

Formule de l'équation quadratique:

Pour

a = - 18808.4736, b = - 3031.2576, c = 13368.3696

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm ( - 3031.2576 ) ^{2} - 4 ( - 18808.4736 ) \cdot 13368.3696}{2 ( - 18808.4736 )}

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm ( - 3031.2576 ) ^{2} - 4 ( - 18808.4736 ) \cdot 13368.3696}{2 ( - 18808.4736 )}

(- 3031.2576)^{2} - 4 (- 18808.4736) \cdot 13368.3696 = 1014943029.424128

(- 3031.2576)^{2} - 4 (- 18808.4736) \cdot 13368.3696

Appliquer la règle

- (- a) = a

= (- 3031.2576)^{2} + 4 \cdot 18808.4736 \cdot 13368.3696

Appliquer la règle de l'exposant:

(- a)^{n} = a^{n},

n

pair

(- 3031.2576)^{2} = 3031.257 6^{2}

= 3031.257 6^{2} + 4 \cdot 13368.3696 \cdot 18808.4736

Multiplier les nombres :

4 \cdot 18808.4736 \cdot 13368.3696 = 1005754506.78657 \dots

= 3031.257 6^{2} + 1005754506.78657 \dots

3031.257 6^{2} = 9188522.63755 \dots

= 9188522.63755 \dots + 1005754506.78657 \dots

Additionner les nombres :

9188522.63755 \dots + 1005754506.78657 \dots = 1014943029.424128

= 1014943029.424128

u_{1, 2} = \frac{- ( - 3031.2576 ) \pm 1014943029.424128}{2 ( - 18808.4736 )}

Séparer les solutions

u_{1} = \frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )}, u_{2} = \frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )}

u = \frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )} : - \frac{3031.2576 + 1014943029.424128}{37616.9472}

\frac{- ( - 3031.2576 ) + 1014943029.424128}{2 ( - 18808.4736 )}

Retirer les parenthèses:

(- a) = - a, - (- a) = a

= \frac{3031.2576 + 1014943029.424128}{- 2 \cdot 18808.4736}

Multiplier les nombres :

2 \cdot 18808.4736 = 37616.9472

= \frac{3031.2576 + 1014943029.424128}{- 37616.9472}

Appliquer la règle des fractions:

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

= - \frac{3031.2576 + 1014943029.424128}{37616.9472}

u = \frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )} : \frac{1014943029.424128 - 3031.2576}{37616.9472}

\frac{- ( - 3031.2576 ) - 1014943029.424128}{2 ( - 18808.4736 )}

Retirer les parenthèses:

(- a) = - a, - (- a) = a

= \frac{3031.2576 - 1014943029.424128}{- 2 \cdot 18808.4736}

Multiplier les nombres :

2 \cdot 18808.4736 = 37616.9472

= \frac{3031.2576 - 1014943029.424128}{- 37616.9472}

Appliquer la règle des fractions:

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

3031.2576 - 1014943029.424128 = - (1014943029.424128 - 3031.2576)

= \frac{1014943029.424128 - 3031.2576}{37616.9472}

Les solutions de l'équation de forme quadratique sont :

u = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, u = \frac{1014943029.424128 - 3031.2576}{37616.9472}

Remplacer

u = cos (a)

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472} : a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

Appliquer les propriétés trigonométriques inverses

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

Solutions générales pour

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472} : a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

Appliquer les propriétés trigonométriques inverses

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

Solutions générales pour

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Combiner toutes les solutions

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Vérifier les solutions en les intégrant dans l'équation d'origine

Vérifier des solutions en les intégrant dans

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

Retirer celles qui ne répondent pas à l'équation.

Vérifier la solution

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn :

Faux

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

Insérer

n = 1

arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

Pour

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

insérer

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

Redéfinir

109.40771 \dots = 21.48

\Rightarrow Faux

Vérifier la solution

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn :

vrai

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

Insérer

n = 1

- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

Pour

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

insérer

a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (- arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

Redéfinir

21.48 = 21.48

\Rightarrow vrai

Vérifier la solution

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn :

vrai

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Insérer

n = 1

arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

Pour

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

insérer

a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

Redéfinir

21.48 = 21.48

\Rightarrow vrai

Vérifier la solution

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn :

Faux

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Insérer

n = 1

2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

Pour

129.8 sin (a) - 0.6129.8 cos (a) = 121.79

insérer

a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1

12 \cdot 9.8 sin (2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) - 0.6 \cdot 12 \cdot 9.8 cos (2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 π 1) = 12 \cdot 1.79

Redéfinir

- 129.62418 \dots = 21.48

\Rightarrow Faux

a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Montrer les solutions sous la forme décimale

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

Graphe

Exemples populaires

solvefor v,a=arctan((v^2)/(gR))

so l v e f or v, a = arctan (\frac{v ^{2}}{g R})

3sin^2(x)=4sin(x)

3 sin^{2} (x) = 4 sin (x)

2cos^2(x)-7cos(x)=0

2 cos^{2} (x) - 7 cos (x) = 0

tan(x)=tan(2x)

tan (x) = tan (2 x)

2cos(x)= 1/2

2 cos (x) = \frac{1}{2}

12*9.8*sin(a)-0.6*12*9.8*cos(a)=12*1.79

Solution

Solution

Graphe

Exemples populaires

129.8sin(a)-0.6129.8cos(a)=121.79