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Popular >

sqrt(3)= pi/3 sec^2(c)

Solución

3 = \frac{π}{3} sec^{2} (c)

Solución

c = 0.68001 \dots + 2 πn, c = 2 π - 0.68001 \dots + 2 πn, c = 2.46157 \dots + 2 πn, c = - 2.46157 \dots + 2 πn

+1

Grados

c = 38.96227 \dots^{\circ} + 36 0^{\circ} n, c = 321.03772 \dots^{\circ} + 36 0^{\circ} n, c = 141.03772 \dots^{\circ} + 36 0^{\circ} n, c = - 141.03772 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

3 = \frac{π}{3} sec^{2} (c)

Intercambiar lados

\frac{π}{3} sec^{2} (c) = 3

Usando el método de sustitución

\frac{π}{3} sec^{2} (c) = 3

Sea:

sec (c) = u

\frac{π}{3} u^{2} = 3

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

\frac{π}{3} u^{2} = 3

Multiplicar ambos lados por

3

\frac{π}{3} u^{2} = 3

Multiplicar ambos lados por

3

3 \cdot \frac{π}{3} u^{2} = 33

Simplificar

π u^{2} = 33

π u^{2} = 33

Dividir ambos lados entre

π

π u^{2} = 33

Dividir ambos lados entre

π

\frac{π u ^{2}}{π} = \frac{3 3}{π}

Simplificar

u^{2} = \frac{3 3}{π}

u^{2} = \frac{3 3}{π}

Para

x^{2} = f (a)

las soluciones son

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

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

Sustituir en la ecuación

u = sec (c)

sec (c) = \frac{3 3}{π}, sec (c) = - \frac{3 3}{π}

sec (c) = \frac{3 3}{π}, sec (c) = - \frac{3 3}{π}

sec (c) = \frac{3 3}{π} : c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (c) = \frac{3 3}{π}

Aplicar propiedades trigonométricas inversas

sec (c) = \frac{3 3}{π}

Soluciones generales para

sec (c) = \frac{3 3}{π}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (c) = - \frac{3 3}{π} : c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

sec (c) = - \frac{3 3}{π}

Aplicar propiedades trigonométricas inversas

sec (c) = - \frac{3 3}{π}

Soluciones generales para

sec (c) = - \frac{3 3}{π}

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

Combinar toda las soluciones

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn, c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

Mostrar soluciones en forma decimal

c = 0.68001 \dots + 2 πn, c = 2 π - 0.68001 \dots + 2 πn, c = 2.46157 \dots + 2 πn, c = - 2.46157 \dots + 2 πn

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(sin(90))/(3.37)=(sin(x))/(0.7)

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

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