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Popular >

-15+4cos(θ)=-15-2sqrt(2)

Solución

- 15 + 4 cos (θ) = - 15 - 22

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Grados

θ = 13 5^{\circ} + 36 0^{\circ} n, θ = 22 5^{\circ} + 36 0^{\circ} n

Pasos de solución

- 15 + 4 cos (θ) = - 15 - 22

Sumar

15

a ambos lados

- 15 + 4 cos (θ) + 15 = - 15 - 22 + 15

Simplificar

4 cos (θ) = - 22

Dividir ambos lados entre

4

4 cos (θ) = - 22

Dividir ambos lados entre

4

\frac{4 cos ( θ )}{4} = \frac{- 2 2}{4}

Simplificar

\frac{4 cos ( θ )}{4} = \frac{- 2 2}{4}

Simplificar

\frac{4 cos ( θ )}{4} : cos (θ)

\frac{4 cos ( θ )}{4}

Dividir:

\frac{4}{4} = 1

= cos (θ)

Simplificar

\frac{- 2 2}{4} : - \frac{2}{2}

\frac{- 2 2}{4}

Aplicar las propiedades de las fracciones:

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

= - \frac{2 2}{4}

Eliminar los terminos comunes:

2

= - \frac{2}{2}

cos (θ) = - \frac{2}{2}

cos (θ) = - \frac{2}{2}

cos (θ) = - \frac{2}{2}

Soluciones generales para

cos (θ) = - \frac{2}{2}

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

cos (2 x) = 1 - 3 sin (x)

3 sin^{2} (x) - 7 sin (x) - 2 = 0

3 sin (2 t) + 4 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

sin^{2} (z) = - 1

2 cos (x) + sin (x) = 1