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5-tan^2(x)=4,0<= x<= 360

Solución

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

Solución

x = 4 5^{\circ}, x = 22 5^{\circ}, x = 13 5^{\circ}, x = 31 5^{\circ}

+1

radianes

x = \frac{π}{4}, x = \frac{5 π}{4}, x = \frac{3 π}{4}, x = \frac{7 π}{4}

Pasos de solución

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

Usando el método de sustitución

5 - tan^{2} (x) = 4

Sea:

tan (x) = u

5 - u^{2} = 4

5 - u^{2} = 4 : u = 1, u = - 1

5 - u^{2} = 4

Mover

5

al lado derecho

5 - u^{2} = 4

Restar

5

de ambos lados

5 - u^{2} - 5 = 4 - 5

Simplificar

- u^{2} = - 1

- u^{2} = - 1

Dividir ambos lados entre

- 1

- u^{2} = - 1

Dividir ambos lados entre

- 1

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

Simplificar

u^{2} = 1

u^{2} = 1

Para

x^{2} = f (a)

las soluciones son

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

u = 1, u = - 1

1 = 1

1

Aplicar la regla

1 = 1

= 1

- 1 = - 1

- 1

Aplicar la regla

1 = 1

= - 1

u = 1, u = - 1

Sustituir en la ecuación

u = tan (x)

tan (x) = 1, tan (x) = - 1

tan (x) = 1, tan (x) = - 1

tan (x) = 1, 0 \leq x \leq 36 0^{\circ} : x = 4 5^{\circ}, x = 22 5^{\circ}

tan (x) = 1, 0 \leq x \leq 36 0^{\circ}

Soluciones generales para

tan (x) = 1

tan (x)

tabla de valores periódicos con

18 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 4 5^{\circ} + 18 0^{\circ} n

x = 4 5^{\circ} + 18 0^{\circ} n

Soluciones para el rango

0 \leq x \leq 36 0^{\circ}

x = 4 5^{\circ}, x = 22 5^{\circ}

tan (x) = - 1, 0 \leq x \leq 36 0^{\circ} : x = 13 5^{\circ}, x = 31 5^{\circ}

tan (x) = - 1, 0 \leq x \leq 36 0^{\circ}

Soluciones generales para

tan (x) = - 1

tan (x)

tabla de valores periódicos con

18 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 13 5^{\circ} + 18 0^{\circ} n

x = 13 5^{\circ} + 18 0^{\circ} n

Soluciones para el rango

0 \leq x \leq 36 0^{\circ}

x = 13 5^{\circ}, x = 31 5^{\circ}

Combinar toda las soluciones

x = 4 5^{\circ}, x = 22 5^{\circ}, x = 13 5^{\circ}, x = 31 5^{\circ}

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