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Popular Trigonometria >

3.8=11.8sin(3.92232*t)

Solução

3.8 = 11.8 sin (3.92232 \cdot t)

Solução

t = \frac{0.32787 \dots}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{0.32787 \dots}{3.92232} + \frac{2 πn}{3.92232}

Graus

t = 4.78950 \dots^{\circ} + 91.78241 \dots^{\circ} n, t = 41.10170 \dots^{\circ} + 91.78241 \dots^{\circ} n

Passos da solução

3.8 = 11.8 sin (3.92232 t)

Trocar lados

11.8 sin (3.92232 t) = 3.8

Multiplicar ambos os lados por

10

11.8 sin (3.92232 t) = 3.8

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

11.8 sin (3.92232 t) \cdot 10 = 3.8 \cdot 10

Simplificar

118 sin (3.92232 t) = 38

118 sin (3.92232 t) = 38

Dividir ambos os lados por

118

118 sin (3.92232 t) = 38

Dividir ambos os lados por

118

\frac{118 sin ( 3.92232 t )}{118} = \frac{38}{118}

Simplificar

sin (3.92232 t) = \frac{19}{59}

sin (3.92232 t) = \frac{19}{59}

Aplique as propriedades trigonométricas inversas

sin (3.92232 t) = \frac{19}{59}

Soluções gerais para

sin (3.92232 t) = \frac{19}{59}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

3.92232 t = arcsin (\frac{19}{59}) + 2 πn, 3.92232 t = π - arcsin (\frac{19}{59}) + 2 πn

3.92232 t = arcsin (\frac{19}{59}) + 2 πn, 3.92232 t = π - arcsin (\frac{19}{59}) + 2 πn

Resolver

3.92232 t = arcsin (\frac{19}{59}) + 2 πn : t = \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

3.92232 t = arcsin (\frac{19}{59}) + 2 πn

Dividir ambos os lados por

3.92232

3.92232 t = arcsin (\frac{19}{59}) + 2 πn

Dividir ambos os lados por

3.92232

\frac{3.92232 t}{3.92232} = \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

Simplificar

t = \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

Resolver

3.92232 t = π - arcsin (\frac{19}{59}) + 2 πn : t = \frac{π}{3.92232} - \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

3.92232 t = π - arcsin (\frac{19}{59}) + 2 πn

Dividir ambos os lados por

3.92232

3.92232 t = π - arcsin (\frac{19}{59}) + 2 πn

Dividir ambos os lados por

3.92232

\frac{3.92232 t}{3.92232} = \frac{π}{3.92232} - \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

Simplificar

t = \frac{π}{3.92232} - \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{π}{3.92232} - \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{arcsin ( \frac{19}{59} )}{3.92232} + \frac{2 πn}{3.92232}

Mostrar soluções na forma decimal

t = \frac{0.32787 \dots}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{0.32787 \dots}{3.92232} + \frac{2 πn}{3.92232}

Gráfico

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