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Popular >

h=3sin(2x-1)+4

Solution

h = 3 sin (2 x - 1) + 4

Solution

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}, x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

Solution steps

h = 3 sin (2 x - 1) + 4

Switch sides

3 sin (2 x - 1) + 4 = h

Move

4

to the right side

3 sin (2 x - 1) + 4 = h

Subtract

4

from both sides

3 sin (2 x - 1) + 4 - 4 = h - 4

Simplify

3 sin (2 x - 1) = h - 4

3 sin (2 x - 1) = h - 4

Divide both sides by

3

3 sin (2 x - 1) = h - 4

Divide both sides by

3

\frac{3 sin ( 2 x - 1 )}{3} = \frac{h}{3} - \frac{4}{3}

Simplify

\frac{3 sin ( 2 x - 1 )}{3} = \frac{h}{3} - \frac{4}{3}

Simplify

\frac{3 sin ( 2 x - 1 )}{3} : sin (2 x - 1)

\frac{3 sin ( 2 x - 1 )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sin (2 x - 1)

Simplify

\frac{h}{3} - \frac{4}{3} : \frac{h - 4}{3}

\frac{h}{3} - \frac{4}{3}

Apply rule

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

= \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

sin (2 x - 1) = \frac{h - 4}{3}

Apply trig inverse properties

sin (2 x - 1) = \frac{h - 4}{3}

General solutions for

sin (2 x - 1) = \frac{h - 4}{3}

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

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn, 2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn, 2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Solve

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn : x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn

Move

1

to the right side

2 x - 1 = arcsin (\frac{h - 4}{3}) + 2 πn

Add

1

to both sides

2 x - 1 + 1 = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Simplify

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Divide both sides by

2

2 x = arcsin (\frac{h - 4}{3}) + 2 πn + 1

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplify

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}

Solve

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn : x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Move

1

to the right side

2 x - 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn

Add

1

to both sides

2 x - 1 + 1 = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Simplify

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Divide both sides by

2

2 x = π + arcsin (- \frac{h - 4}{3}) + 2 πn + 1

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplify

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2} : \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2} + \frac{2 πn}{2} + \frac{1}{2}

Group like terms

= \frac{π}{2} + \frac{1}{2} + \frac{2 πn}{2} + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

x = \frac{arcsin ( \frac{h - 4}{3} )}{2} + πn + \frac{1}{2}, x = \frac{π}{2} + \frac{1}{2} + πn + \frac{arcsin ( - \frac{h - 4}{3} )}{2}

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