What is the general solution for 3sin(2((x-pi)/2))+1=2,5 ?

The general solution for 3sin(2((x-pi)/2))+1=2,5 is No Solution for x\in\mathbb{R}

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3sin(2((x-pi)/2))+1=2,5

Solution

3 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

Solution

No Solution for x \in R

Solution steps

3 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

Move

1

to the right side

3 sin (2 \frac{x - π}{2}) + 1 = 2

Subtract

1

from both sides

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

Simplify

3 sin (2 \frac{x - π}{2}) = 1

3 sin (2 \frac{x - π}{2}) = 1

Divide both sides by

3

3 sin (2 \frac{x - π}{2}) = 1

Divide both sides by

3

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

Simplify

sin (2 \frac{x - π}{2}) = \frac{1}{3}

sin (2 \frac{x - π}{2}) = \frac{1}{3}

Apply trig inverse properties

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

General solutions for

sin (2 \frac{x - π}{2}) = \frac{1}{3}

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

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

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

Solve

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

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

Multiply fractions:

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

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

Cancel the common factor:

2

x - π = arcsin (\frac{1}{3}) + 2 πn

Move

π

to the right side

x - π = arcsin (\frac{1}{3}) + 2 πn

Add

π

to both sides

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

Simplify

x = arcsin (\frac{1}{3}) + 2 πn + π

x = arcsin (\frac{1}{3}) + 2 πn + π

Solve

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

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

Multiply fractions:

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

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

Cancel the common factor:

2

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

Move

π

to the right side

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

Add

π

to both sides

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

Simplify

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

Simplify

x - π + π : x

x - π + π

Add similar elements:

- π + π = 0

= x

Simplify

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

π - arcsin (\frac{1}{3}) + 2 πn + π

Group like terms

= π + π + 2 πn - arcsin (\frac{1}{3})

Add similar elements:

π + π = 2 π

= 2 π + 2 πn - arcsin (\frac{1}{3})

x = 2 π + 2 πn - arcsin (\frac{1}{3})

x = 2 π + 2 πn - arcsin (\frac{1}{3})

x = 2 π + 2 πn - arcsin (\frac{1}{3})

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

Solutions for the range

5

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the general solution for 3sin(2((x-pi)/2))+1=2,5 ?
The general solution for 3sin(2((x-pi)/2))+1=2,5 is No Solution for x\in\mathbb{R}