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

The general solution for 5sin(2x-pi/2)=0.5 is x=pin+pi/4+(0.10016…)/2 ,x=pin+pi/2+pi/4-(0.10016…)/2

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Popular >

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

Solution

5 sin (2 x - \frac{π}{2}) = 0.5

Solution

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

Degrees

x = 47.86958 \dots^{\circ} + 18 0^{\circ} n, x = 132.13041 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 sin (2 x - \frac{π}{2}) = 0.5

Divide both sides by

5

5 sin (2 x - \frac{π}{2}) = 0.5

Divide both sides by

5

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

Simplify

sin (2 x - \frac{π}{2}) = 0.1

sin (2 x - \frac{π}{2}) = 0.1

Apply trig inverse properties

sin (2 x - \frac{π}{2}) = 0.1

General solutions for

sin (2 x - \frac{π}{2}) = 0.1

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

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

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

Solve

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

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

Move

\frac{π}{2}

to the right side

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

Add

\frac{π}{2}

to both sides

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

Simplify

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

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

Group like terms

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

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

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

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

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

Solve

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

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

Move

\frac{π}{2}

to the right side

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

Add

\frac{π}{2}

to both sides

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

Simplify

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

Group like terms

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

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

Group like terms

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

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

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

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

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

Show solutions in decimal form

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

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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=pin+pi/4+(0.10016…)/2 ,x=pin+pi/2+pi/4-(0.10016…)/2