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Popular >

sin^2(x)+cos^2(2/5)=1

Solución

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

Solución

x = 0.4 + 2 πn, x = π - 0.4 + 2 πn, x = - 0.4 + 2 πn, x = π + 0.4 + 2 πn

+1

Grados

x = 22.91831 \dots^{\circ} + 36 0^{\circ} n, x = 157.08168 \dots^{\circ} + 36 0^{\circ} n, x = - 22.91831 \dots^{\circ} + 36 0^{\circ} n, x = 202.91831 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Usando el método de sustitución

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

Sea:

sin (x) = u

u^{2} + cos^{2} (\frac{2}{5}) = 1

u^{2} + cos^{2} (\frac{2}{5}) = 1 : u = 1 - cos^{2} (\frac{2}{5}), u = - 1 - cos^{2} (\frac{2}{5})

u^{2} + cos^{2} (\frac{2}{5}) = 1

Mover

cos^{2} (\frac{2}{5})

al lado derecho

u^{2} + cos^{2} (\frac{2}{5}) = 1

Restar

cos^{2} (\frac{2}{5})

de ambos lados

u^{2} + cos^{2} (\frac{2}{5}) - cos^{2} (\frac{2}{5}) = 1 - cos^{2} (\frac{2}{5})

Simplificar

u^{2} = 1 - cos^{2} (\frac{2}{5})

u^{2} = 1 - cos^{2} (\frac{2}{5})

Para

x^{2} = f (a)

las soluciones son

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

u = 1 - cos^{2} (\frac{2}{5}), u = - 1 - cos^{2} (\frac{2}{5})

Sustituir en la ecuación

u = sin (x)

sin (x) = 1 - cos^{2} (\frac{2}{5}), sin (x) = - 1 - cos^{2} (\frac{2}{5})

sin (x) = 1 - cos^{2} (\frac{2}{5}), sin (x) = - 1 - cos^{2} (\frac{2}{5})

sin (x) = 1 - cos^{2} (\frac{2}{5}) : x = arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π - arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

sin (x) = 1 - cos^{2} (\frac{2}{5})

Aplicar propiedades trigonométricas inversas

sin (x) = 1 - cos^{2} (\frac{2}{5})

Soluciones generales para

sin (x) = 1 - cos^{2} (\frac{2}{5})

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π - arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

x = arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π - arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

sin (x) = - 1 - cos^{2} (\frac{2}{5}) : x = arcsin (- 1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π + arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

sin (x) = - 1 - cos^{2} (\frac{2}{5})

Aplicar propiedades trigonométricas inversas

sin (x) = - 1 - cos^{2} (\frac{2}{5})

Soluciones generales para

sin (x) = - 1 - cos^{2} (\frac{2}{5})

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- 1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π + arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

x = arcsin (- 1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π + arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

Combinar toda las soluciones

x = arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π - arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn, x = arcsin (- 1 - cos^{2} (\frac{2}{5})) + 2 πn, x = π + arcsin (1 - cos^{2} (\frac{2}{5})) + 2 πn

Mostrar soluciones en forma decimal

x = 0.4 + 2 πn, x = π - 0.4 + 2 πn, x = - 0.4 + 2 πn, x = π + 0.4 + 2 πn

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