What is the general solution for solvefor x,Y=0.5sin(3.07x-2.4t+0.59) ?

The general solution for solvefor x,Y=0.5sin(3.07x-2.4t+0.59) is

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solvefor x,Y=0.5sin(3.07x-2.4t+0.59)

Solution

solve for

x, Y = 0.5 sin (3.07 x - 2.4 t + 0.59)

Solution

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}, x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

Solution steps

Y = 0.5 sin (3.07 x - 2.4 t + 0.59)

Switch sides

0.5 sin (3.07 x - 2.4 t + 0.59) = Y

Multiply both sides by

10

0.5 sin (3.07 x - 2.4 t + 0.59) = Y

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

0.5 sin (3.07 x - 2.4 t + 0.59) \cdot 10 = Y \cdot 10

Refine

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

Divide both sides by

5

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

Divide both sides by

5

\frac{5 sin ( 3.07 x - 2.4 t + 0.59 )}{5} = \frac{Y \cdot 10}{5}

Simplify

sin (3.07 x - 2.4 t + 0.59) = 2 Y

sin (3.07 x - 2.4 t + 0.59) = 2 Y

Apply trig inverse properties

sin (3.07 x - 2.4 t + 0.59) = 2 Y

General solutions for

sin (3.07 x - 2.4 t + 0.59) = 2 Y

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

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn, 3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn, 3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

Solve

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn : x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn

Move

2.4 t

to the right side

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn

Add

2.4 t

to both sides

3.07 x - 2.4 t + 0.59 + 2.4 t = arcsin (2 Y) + 2 πn + 2.4 t

Simplify

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

Move

0.59

to the right side

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

Subtract

0.59

from both sides

3.07 x + 0.59 - 0.59 = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

Simplify

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

Divide both sides by

3.07

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

Divide both sides by

3.07

\frac{3.07 x}{3.07} = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

Simplify

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

Solve

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn : x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

Move

2.4 t

to the right side

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

Add

2.4 t

to both sides

3.07 x - 2.4 t + 0.59 + 2.4 t = π + arcsin (- 2 Y) + 2 πn + 2.4 t

Simplify

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

Move

0.59

to the right side

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

Subtract

0.59

from both sides

3.07 x + 0.59 - 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

Simplify

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

Divide both sides by

3.07

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

Divide both sides by

3.07

\frac{3.07 x}{3.07} = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

Simplify

x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}, x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,Y=0.5sin(3.07x-2.4t+0.59) ?
The general solution for solvefor x,Y=0.5sin(3.07x-2.4t+0.59) is