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Popolare Trigonometria >

solvefor t,y=3sin(2t-pi/4)

Soluzione

risolvere per

t, y = 3 sin (2 t - \frac{π}{4})

Soluzione

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}, t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

Fasi della soluzione

y = 3 sin (2 t - \frac{π}{4})

Scambia i lati

3 sin (2 t - \frac{π}{4}) = y

Dividere entrambi i lati per

3

3 sin (2 t - \frac{π}{4}) = y

Dividere entrambi i lati per

3

\frac{3 sin ( 2 t - \frac{π}{4} )}{3} = \frac{y}{3}

Semplificare

sin (2 t - \frac{π}{4}) = \frac{y}{3}

sin (2 t - \frac{π}{4}) = \frac{y}{3}

Applica le proprietà inverse delle funzioni trigonometriche

sin (2 t - \frac{π}{4}) = \frac{y}{3}

Soluzioni generali per

sin (2 t - \frac{π}{4}) = \frac{y}{3}

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

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn, 2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn, 2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

Risolvi

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn : t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn

Spostare

\frac{π}{4}

a destra dell'equazione

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn

Aggiungi

\frac{π}{4}

ad entrambi i lati

2 t - \frac{π}{4} + \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

Semplificare

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

Dividere entrambi i lati per

2

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

Dividere entrambi i lati per

2

\frac{2 t}{2} = \frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

Semplificare

\frac{2 t}{2} = \frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

Semplificare

\frac{2 t}{2} : t

\frac{2 t}{2}

Dividi i numeri:

\frac{2}{2} = 1

= t

Semplificare

\frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} : \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

\frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividi i numeri:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Applica la regola delle frazioni:

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

= \frac{π}{4 \cdot 2}

Moltiplica i numeri:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

Risolvi

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn : t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

Spostare

\frac{π}{4}

a destra dell'equazione

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

Aggiungi

\frac{π}{4}

ad entrambi i lati

2 t - \frac{π}{4} + \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

Semplificare

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

Dividere entrambi i lati per

2

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

Dividere entrambi i lati per

2

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

Semplificare

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

Semplificare

\frac{2 t}{2} : t

\frac{2 t}{2}

Dividi i numeri:

\frac{2}{2} = 1

= t

Semplificare

\frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} : πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

Raggruppa termini simili

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} + \frac{arcsin ( - \frac{y}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividi i numeri:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Applica la regola delle frazioni:

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

= \frac{π}{4 \cdot 2}

Moltiplica i numeri:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{π}{2} + πn + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

Raggruppa termini simili

= πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}, t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

Grafico

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