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Popular >

3(cos(x)-1)=-1

Solución

3 (cos (x) - 1) = - 1

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Grados

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

3 (cos (x) - 1) = - 1

Dividir ambos lados entre

3

3 (cos (x) - 1) = - 1

Dividir ambos lados entre

3

\frac{3 ( cos ( x ) - 1 )}{3} = \frac{- 1}{3}

Simplificar

cos (x) - 1 = - \frac{1}{3}

cos (x) - 1 = - \frac{1}{3}

Mover

1

al lado derecho

cos (x) - 1 = - \frac{1}{3}

Sumar

1

a ambos lados

cos (x) - 1 + 1 = - \frac{1}{3} + 1

Simplificar

cos (x) - 1 + 1 = - \frac{1}{3} + 1

Simplificar

cos (x) - 1 + 1 : cos (x)

cos (x) - 1 + 1

Sumar elementos similares:

- 1 + 1 = 0

= cos (x)

Simplificar

- \frac{1}{3} + 1 : \frac{2}{3}

- \frac{1}{3} + 1

Convertir a fracción:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} - \frac{1}{3}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 3 - 1}{3}

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

Multiplicar los numeros:

1 \cdot 3 = 3

= 3 - 1

Restar:

3 - 1 = 2

= 2

= \frac{2}{3}

cos (x) = \frac{2}{3}

cos (x) = \frac{2}{3}

cos (x) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{2}{3}

Soluciones generales para

cos (x) = \frac{2}{3}

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

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

9.6 8^{2} = 12. 5^{2} + 6.4 7^{2} - 2 \cdot 12.5 \cdot 6.47 \cdot cos (θ)

- 4 = \frac{sin ( θ )}{cos ( θ )}

3 = cos (θ)

tan (θ) sin (θ) - 3 sin (θ) = 0

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