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Popular Trigonometría >

solvefor t,0.08=0.1cos(4t)

Solución

resolver para

t, 0.08 = 0.1 cos (4 t)

Solución

t = \frac{0.64350 \dots}{4} + \frac{πn}{2}, t = \frac{π}{2} - \frac{0.64350 \dots}{4} + \frac{πn}{2}

Grados

t = 9.21747 \dots^{\circ} + 9 0^{\circ} n, t = 80.78252 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

0.08 = 0.1 cos (4 t)

Intercambiar lados

0.1 cos (4 t) = 0.08

Multiplicar ambos lados por

100

0.1 cos (4 t) = 0.08

Para eliminar los puntos decimales, multiplique por 10 por cada digito después del punto decimalHay digitos

2

a la derecha del punto decimal, por lo que debe multiplicar por

100

0.1 cos (4 t) \cdot 100 = 0.08 \cdot 100

Simplificar

10 cos (4 t) = 8

10 cos (4 t) = 8

Dividir ambos lados entre

10

10 cos (4 t) = 8

Dividir ambos lados entre

10

\frac{10 cos ( 4 t )}{10} = \frac{8}{10}

Simplificar

cos (4 t) = \frac{4}{5}

cos (4 t) = \frac{4}{5}

Aplicar propiedades trigonométricas inversas

cos (4 t) = \frac{4}{5}

Soluciones generales para

cos (4 t) = \frac{4}{5}

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

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

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

Resolver

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

4 t = arccos (\frac{4}{5}) + 2 πn

Dividir ambos lados entre

4

4 t = arccos (\frac{4}{5}) + 2 πn

Dividir ambos lados entre

4

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

Simplificar

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

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

Resolver

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

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

Dividir ambos lados entre

4

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

Dividir ambos lados entre

4

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

Simplificar

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

Simplificar

\frac{4 t}{4} : t

\frac{4 t}{4}

Dividir:

\frac{4}{4} = 1

= t

Simplificar

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

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

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

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

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

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

Mostrar soluciones en forma decimal

t = \frac{0.64350 \dots}{4} + \frac{πn}{2}, t = \frac{π}{2} - \frac{0.64350 \dots}{4} + \frac{πn}{2}

Gráfica

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