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(cos(270))^{sin(90)}

Solución

(cos (27 0^{\circ}))^{s i n (9 0^{\circ})}

0

Pasos de solución

(cos (27 0^{\circ}))^{s i n (9 0^{\circ})}

= cos^{s i n (9 0^{\circ})} (27 0^{\circ})

Re-escribir usando identidades trigonométricas:

cos (27 0^{\circ}) = 1 - 2 sin^{2} (13 5^{\circ})

cos (27 0^{\circ})

Escribir

cos (27 0^{\circ})

como

cos (2 \cdot 13 5^{\circ})

= cos (2 \cdot 13 5^{\circ})

Utilizar la identidad trigonométrica del ángulo doble:

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

= 1 - 2 sin^{2} (13 5^{\circ})

= (1 - 2 sin^{2} (13 5^{\circ}))^{s i n (9 0^{\circ})}

Utilizar la siguiente identidad trivial:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

tabla de valores periódicos con

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

Utilizar la siguiente identidad trivial:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

tabla de valores periódicos con

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 - 2 (\frac{2}{2})^{2}^{1}

Simplificar

1 - 2 (\frac{2}{2})^{2}^{1} : 0

1 - 2 (\frac{2}{2})^{2}^{1}

Aplicar la regla

a^{1} = a

= 1 - 2 (\frac{2}{2})^{2}

2 (\frac{2}{2})^{2} = 1

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

(\frac{2}{2})^{2} = \frac{1}{2}

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

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 2 ) ^{2}}{2 ^{2}}

(2)^{2} : 2

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 2

= \frac{2}{2 ^{2}}

Eliminar los terminos comunes:

2

= \frac{1}{2}

= 2 \cdot \frac{1}{2}

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 1 - 1

Restar:

1 - 1 = 0

= 0

= 0

sin (π + \frac{π}{6})

sin (\frac{π ^{2}}{3})

cos (arctan (- \frac{4}{3}))

80 cos (0)

sin (2 \frac{2 π}{3})