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(6arcsin(cos((5pi)/3)))/(pi)

Solución

\frac{6 arcsin ( cos ( \frac{5 π}{3} ) )}{π}

1

Notación decimal

57.3

Pasos de solución

\frac{6 arcsin ( cos ( \frac{5 π}{3} ) )}{π}

Re-escribir usando identidades trigonométricas:

arcsin (cos (\frac{5 π}{3})) = \frac{π}{6}

arcsin (cos (\frac{5 π}{3}))

Re-escribir usando identidades trigonométricas:

cos (\frac{5 π}{3}) = sin (- \frac{7 π}{6})

cos (\frac{5 π}{3})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{5 π}{3})

= sin (- \frac{7 π}{6})

= arcsin (sin (- \frac{7 π}{6}))

Use the inverse trig property:

\frac{π}{6}

arcsin (sin (- \frac{7 π}{6}))

Para

- \frac{π}{2} \leq x \leq \frac{π}{2}

a rcs in (s in (x)) = x

Re-escribir usando identidades trigonométricas:

sin (- \frac{7 π}{6}) = sin (\frac{π}{6})

sin (- \frac{7 π}{6})

sin (x) = sin (π - (x))

= sin (\frac{7 π}{6} - π)

= sin (\frac{π}{6})

= arcsin (sin (\frac{π}{6}))

- \frac{π}{2} \leq \frac{π}{6} \leq \frac{π}{2}

= \frac{π}{6}

= \frac{π}{6}

= \frac{6 \cdot \frac{π}{6}}{π}

Simplificar

\frac{6 \cdot \frac{π}{6}}{π} : 1

\frac{6 \cdot \frac{π}{6}}{π}

Multiplicar

6 \cdot \frac{π}{6} : π

6 \cdot \frac{π}{6}

Multiplicar fracciones:

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

= \frac{π 6}{6}

Eliminar los terminos comunes:

6

= π

= \frac{π}{π}

Aplicar la regla

\frac{a}{a} = 1

= 1

= 1

\frac{5}{tan ( 22. 5 ^{\circ} )}

\frac{1}{3} (arctan (6^{3}) - arctan (1^{3}))

1 + tan^{2} (4 5^{\circ})

40 sin (7 2^{\circ})

sin (4 5^{\circ}) - sin (4 5^{\circ})