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Popular Trigonometría >

cos^2(θ)= 1/3

Solución

cos^{2} (θ) = \frac{1}{3}

Solución

θ = 0.95531 \dots + 2 πn, θ = 2 π - 0.95531 \dots + 2 πn, θ = 2.18627 \dots + 2 πn, θ = - 2.18627 \dots + 2 πn

+1

Grados

θ = 54.73561 \dots^{\circ} + 36 0^{\circ} n, θ = 305.26438 \dots^{\circ} + 36 0^{\circ} n, θ = 125.26438 \dots^{\circ} + 36 0^{\circ} n, θ = - 125.26438 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

cos^{2} (θ) = \frac{1}{3}

Usando el método de sustitución

cos^{2} (θ) = \frac{1}{3}

Sea:

cos (θ) = u

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3} : u = \frac{1}{3}, u = - \frac{1}{3}

u^{2} = \frac{1}{3}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = \frac{1}{3}, u = - \frac{1}{3}

Sustituir en la ecuación

u = cos (θ)

cos (θ) = \frac{1}{3}, cos (θ) = - \frac{1}{3}

cos (θ) = \frac{1}{3}, cos (θ) = - \frac{1}{3}

cos (θ) = \frac{1}{3} : θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

cos (θ) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (θ) = \frac{1}{3}

Soluciones generales para

cos (θ) = \frac{1}{3}

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

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

cos (θ) = - \frac{1}{3} : θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

cos (θ) = - \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (θ) = - \frac{1}{3}

Soluciones generales para

cos (θ) = - \frac{1}{3}

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

θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

Combinar toda las soluciones

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn, θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0.95531 \dots + 2 πn, θ = 2 π - 0.95531 \dots + 2 πn, θ = 2.18627 \dots + 2 πn, θ = - 2.18627 \dots + 2 πn

Gráfica

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