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cos(α)=sqrt((1+1/5)/2)

Solución

cos (α) = \frac{1 + \frac{1}{5}}{2}

α = 0.68471 \dots + 2 πn, α = 2 π - 0.68471 \dots + 2 πn

Grados

α = 39.23152 \dots^{\circ} + 36 0^{\circ} n, α = 320.76847 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

cos (α) = \frac{1 + \frac{1}{5}}{2}

\frac{1 + \frac{1}{5}}{2} = \frac{3}{5}

\frac{1 + \frac{1}{5}}{2}

Simplificar

1 + \frac{1}{5}

en una fracción:

\frac{6}{5}

1 + \frac{1}{5}

Convertir a fracción:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} + \frac{1}{5}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{1 \cdot 5 + 1}{5}

1 \cdot 5 + 1 = 6

1 \cdot 5 + 1

Multiplicar los numeros:

1 \cdot 5 = 5

= 5 + 1

Sumar:

5 + 1 = 6

= 6

= \frac{6}{5}

= \frac{\frac{6}{5}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{6}{5 \cdot 2}

Multiplicar los numeros:

5 \cdot 2 = 10

= \frac{6}{10}

Eliminar los terminos comunes:

2

= \frac{3}{5}

cos (α) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

cos (α) = \frac{3}{5}

Soluciones generales para

cos (α) = \frac{3}{5}

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

α = arccos (\frac{3}{5}) + 2 πn, α = 2 π - arccos (\frac{3}{5}) + 2 πn

α = arccos (\frac{3}{5}) + 2 πn, α = 2 π - arccos (\frac{3}{5}) + 2 πn

Mostrar soluciones en forma decimal

α = 0.68471 \dots + 2 πn, α = 2 π - 0.68471 \dots + 2 πn

(tan (x)) (sin^{2} (x) - a) (sec (x) - a) = 0, 0 < a < 1

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

sin (\cdot + \frac{π}{2}) = cos (x)

sin (θ) = (0.000069) 2 (500 \cdot 1 0^{- 9})

(2 sin^{2} (x) - 1) (tan (x) - 1) = 0