What is the general solution for 5sin((2x-pi)/2)=0.5 ?

The general solution for 5sin((2x-pi)/2)=0.5 is x= pi/2+2pin+0.10016…,x=(3pi)/2+2pin-0.10016…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5sin((2x-pi)/2)=0.5

Solution

5 sin (\frac{2 x - π}{2}) = 0.5

Solution

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

Degrees

x = 95.73917 \dots^{\circ} + 36 0^{\circ} n, x = 264.26082 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sin (\frac{2 x - π}{2}) = 0.5

Divide both sides by

5

5 sin (\frac{2 x - π}{2}) = 0.5

Divide both sides by

5

\frac{5 sin ( \frac{2 x - π}{2} )}{5} = \frac{0.5}{5}

Simplify

sin (\frac{2 x - π}{2}) = 0.1

sin (\frac{2 x - π}{2}) = 0.1

Apply trig inverse properties

sin (\frac{2 x - π}{2}) = 0.1

General solutions for

sin (\frac{2 x - π}{2}) = 0.1

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

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn, \frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn, \frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn

Solve

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn : x = \frac{π}{2} + 2 πn + arcsin (0.1)

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn

Multiply both sides by

2

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn

Multiply both sides by

2

\frac{2 ( 2 x - π )}{2} = 2 arcsin (0.1) + 2 \cdot 2 πn

Simplify

2 x - π = 2 arcsin (0.1) + 4 πn

2 x - π = 2 arcsin (0.1) + 4 πn

Move

π

to the right side

2 x - π = 2 arcsin (0.1) + 4 πn

Add

π

to both sides

2 x - π + π = 2 arcsin (0.1) + 4 πn + π

Simplify

2 x = 2 arcsin (0.1) + 4 πn + π

2 x = 2 arcsin (0.1) + 4 πn + π

Divide both sides by

2

2 x = 2 arcsin (0.1) + 4 πn + π

Divide both sides by

2

\frac{2 x}{2} = \frac{2 arcsin ( 0.1 )}{2} + \frac{4 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{2 arcsin ( 0.1 )}{2} + \frac{4 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{2 arcsin ( 0.1 )}{2} + \frac{4 πn}{2} + \frac{π}{2} : \frac{π}{2} + 2 πn + arcsin (0.1)

\frac{2 arcsin ( 0.1 )}{2} + \frac{4 πn}{2} + \frac{π}{2}

Group like terms

= \frac{π}{2} + \frac{4 πn}{2} + \frac{2 arcsin ( 0.1 )}{2}

Divide the numbers:

\frac{4}{2} = 2

= \frac{π}{2} + 2 πn + \frac{2 arcsin ( 0.1 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1)

Solve

\frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn : x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

\frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn

Multiply both sides by

2

\frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn

Multiply both sides by

2

\frac{2 ( 2 x - π )}{2} = 2 π - 2 arcsin (0.1) + 2 \cdot 2 πn

Simplify

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

Move

π

to the right side

2 x - π = 2 π - 2 arcsin (0.1) + 4 πn

Add

π

to both sides

2 x - π + π = 2 π - 2 arcsin (0.1) + 4 πn + π

Simplify

2 x = 3 π + 4 πn - 2 arcsin (0.1)

2 x = 3 π + 4 πn - 2 arcsin (0.1)

Divide both sides by

2

2 x = 3 π + 4 πn - 2 arcsin (0.1)

Divide both sides by

2

\frac{2 x}{2} = \frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Simplify

\frac{2 x}{2} = \frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2} : \frac{3 π}{2} + 2 πn - arcsin (0.1)

\frac{3 π}{2} + \frac{4 πn}{2} - \frac{2 arcsin ( 0.1 )}{2}

Divide the numbers:

\frac{4}{2} = 2

= \frac{3 π}{2} + 2 πn - \frac{2 arcsin ( 0.1 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1), x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

Show solutions in decimal form

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

Popular Examples

16sin^2(θ)=12

16 sin^{2} (θ) = 12

tan(θ)=-(sqrt(57))/9

tan (θ) = - \frac{57}{9}

sin^2(x)= 2/3

sin^{2} (x) = \frac{2}{3}

sin(4y)+sin(6y)+cos(y)=0

sin (4 y) + sin (6 y) + cos (y) = 0

4cos(x)=sin^2(x)-2-3cos^2(x)

4 cos (x) = sin^{2} (x) - 2 - 3 cos^{2} (x)

Frequently Asked Questions (FAQ)

What is the general solution for 5sin((2x-pi)/2)=0.5 ?
The general solution for 5sin((2x-pi)/2)=0.5 is x= pi/2+2pin+0.10016…,x=(3pi)/2+2pin-0.10016…