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Popular Trigonometría >

6=10cos(4*o)

Solución

6 = 10 cos (4 \cdot o)

Solución

o = \frac{0.92729 \dots}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

+1

Grados

o = 13.28252 \dots^{\circ} + 9 0^{\circ} n, o = 76.71747 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

6 = 10 cos (4 o)

Intercambiar lados

10 cos (4 o) = 6

Dividir ambos lados entre

10

10 cos (4 o) = 6

Dividir ambos lados entre

10

\frac{10 cos ( 4 o )}{10} = \frac{6}{10}

Simplificar

cos (4 o) = \frac{3}{5}

cos (4 o) = \frac{3}{5}

Aplicar propiedades trigonométricas inversas

cos (4 o) = \frac{3}{5}

Soluciones generales para

cos (4 o) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

4 o = arccos (\frac{3}{5}) + 2 πn, 4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

4 o = arccos (\frac{3}{5}) + 2 πn, 4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Resolver

4 o = arccos (\frac{3}{5}) + 2 πn : o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

4 o = arccos (\frac{3}{5}) + 2 πn

Dividir ambos lados entre

4

4 o = arccos (\frac{3}{5}) + 2 πn

Dividir ambos lados entre

4

\frac{4 o}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplificar

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

Resolver

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn : o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Dividir ambos lados entre

4

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Dividir ambos lados entre

4

\frac{4 o}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 o}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 o}{4} : o

\frac{4 o}{4}

Dividir:

\frac{4}{4} = 1

= o

Simplificar

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Cancelar

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar los terminos comunes:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

Mostrar soluciones en forma decimal

o = \frac{0.92729 \dots}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

Gráfica

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