pt

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(pi/6)sin^2(pi/6)

Solução

cos^{2} (\frac{π}{6}) sin^{2} (\frac{π}{6})

Solução

\frac{3}{16}

+1

Notação decimal

0.1875

Passos da solução

cos^{2} (\frac{π}{6}) sin^{2} (\frac{π}{6})

Utilizar a seguinte identidade trivial:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (x)

tabela de periodicidade com ciclo de

2 πn

:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

Utilizar a seguinte identidade trivial:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

tabela de periodicidade com ciclo de

2 πn

:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= (\frac{3}{2})^{2} (\frac{1}{2})^{2}

Simplificar

(\frac{3}{2})^{2} (\frac{1}{2})^{2} : \frac{3}{16}

(\frac{3}{2})^{2} (\frac{1}{2})^{2}

Aplicar as propriedades dos expoentes:

a^{m} b^{m} = (ab)^{m}

(\frac{1}{2})^{2} (\frac{3}{2})^{2} = (\frac{1}{2} \cdot \frac{3}{2})^{2}

= (\frac{1}{2} \cdot \frac{3}{2})^{2}

\frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}

\frac{3}{2} \cdot \frac{1}{2}

Multiplicar frações:

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

= \frac{3 \cdot 1}{2 \cdot 2}

Multiplicar:

3 \cdot 1 = 3

= \frac{3}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{3}{4}

= (\frac{3}{4})^{2}

Aplicar as propriedades dos expoentes:

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

= \frac{( 3 ) ^{2}}{4 ^{2}}

(3)^{2} : 3

Aplicar as propriedades dos radicais:

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

= (3^{\frac{1}{2}})^{2}

Aplicar as propriedades dos expoentes:

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

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

Multiplicar frações:

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

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

Eliminar o fator comum:

2

= 1

= 3

= \frac{3}{4 ^{2}}

4^{2} = 16

= \frac{3}{16}

= \frac{3}{16}

Exemplos populares

tan(arccos((sqrt(2))/3))

tan (arccos (\frac{2}{3}))

10 (cos (3 0^{\circ}))

cot (\frac{2}{3} π)

tan(arctan(pi/4))

tan (arctan (\frac{π}{4}))

1/(sec^2(0+0))-1

\frac{1}{sec ^{2} ( 0 + 0 )} - 1