What is the general solution for 6/pi-4sin(2x)=0 ?

The general solution for 6/pi-4sin(2x)=0 is x=(0.49776…)/2+pin,x= pi/2-(0.49776…)/2+pin

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6/pi-4sin(2x)=0

Solution

\frac{6}{π} - 4 sin (2 x) = 0

Solution

x = \frac{0.49776 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.49776 \dots}{2} + πn

Degrees

x = 14.25997 \dots^{\circ} + 18 0^{\circ} n, x = 75.74002 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{6}{π} - 4 sin (2 x) = 0

Move

\frac{6}{π}

to the right side

\frac{6}{π} - 4 sin (2 x) = 0

Subtract

\frac{6}{π}

from both sides

\frac{6}{π} - 4 sin (2 x) - \frac{6}{π} = 0 - \frac{6}{π}

Simplify

- 4 sin (2 x) = - \frac{6}{π}

- 4 sin (2 x) = - \frac{6}{π}

Divide both sides by

- 4

- 4 sin (2 x) = - \frac{6}{π}

Divide both sides by

- 4

\frac{- 4 sin ( 2 x )}{- 4} = \frac{- \frac{6}{π}}{- 4}

Simplify

\frac{- 4 sin ( 2 x )}{- 4} = \frac{- \frac{6}{π}}{- 4}

Simplify

\frac{- 4 sin ( 2 x )}{- 4} : sin (2 x)

\frac{- 4 sin ( 2 x )}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4 sin ( 2 x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (2 x)

Simplify

\frac{- \frac{6}{π}}{- 4} : \frac{3}{2 π}

\frac{- \frac{6}{π}}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{\frac{6}{π}}{4}

Apply the fraction rule:

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

= \frac{6}{π 4}

Cancel the common factor:

2

= \frac{3}{2 π}

sin (2 x) = \frac{3}{2 π}

sin (2 x) = \frac{3}{2 π}

sin (2 x) = \frac{3}{2 π}

Apply trig inverse properties

sin (2 x) = \frac{3}{2 π}

General solutions for

sin (2 x) = \frac{3}{2 π}

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

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

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

Solve

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

2 x = arcsin (\frac{3}{2 π}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{3}{2 π}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.49776 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.49776 \dots}{2} + πn

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Frequently Asked Questions (FAQ)

What is the general solution for 6/pi-4sin(2x)=0 ?
The general solution for 6/pi-4sin(2x)=0 is x=(0.49776…)/2+pin,x= pi/2-(0.49776…)/2+pin