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Popular Trigonometría >

(4cos(30))^2

Solución

(4 cos (3 0^{\circ}))^{2}

Solución

12

Pasos de solución

(4 cos (3 0^{\circ}))^{2}

Utilizar la siguiente identidad trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} 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}

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

Simplificar

(4 \cdot \frac{3}{2})^{2} : 12

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

Multiplicar

4 \cdot \frac{3}{2} : 23

4 \cdot \frac{3}{2}

Multiplicar fracciones:

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

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

Dividir:

\frac{4}{2} = 2

= 23

= (23)^{2}

Aplicar las leyes de los exponentes:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} (3)^{2}

(3)^{2} : 3

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

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

= 3^{\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

= 3

= 2^{2} \cdot 3

2^{2} = 4

= 4 \cdot 3

Multiplicar los numeros:

4 \cdot 3 = 12

= 12

= 12

Ejemplos populares

(tan(0))/(sec(0))