What is the general solution for 4sin(x/3)-3=0 ?

The general solution for 4sin(x/3)-3=0 is x=3*0.84806…+6pin,x=3pi-3*0.84806…+6pin

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4sin(x/3)-3=0

Solution

4 sin (\frac{x}{3}) - 3 = 0

Solution

x = 3 \cdot 0.84806 \dots + 6 πn, x = 3 π - 3 \cdot 0.84806 \dots + 6 πn

Degrees

x = 145.77113 \dots^{\circ} + 108 0^{\circ} n, x = 394.22886 \dots^{\circ} + 108 0^{\circ} n

Solution steps

4 sin (\frac{x}{3}) - 3 = 0

Move

3

to the right side

4 sin (\frac{x}{3}) - 3 = 0

Add

3

to both sides

4 sin (\frac{x}{3}) - 3 + 3 = 0 + 3

Simplify

4 sin (\frac{x}{3}) = 3

4 sin (\frac{x}{3}) = 3

Divide both sides by

4

4 sin (\frac{x}{3}) = 3

Divide both sides by

4

\frac{4 sin ( \frac{x}{3} )}{4} = \frac{3}{4}

Simplify

sin (\frac{x}{3}) = \frac{3}{4}

sin (\frac{x}{3}) = \frac{3}{4}

Apply trig inverse properties

sin (\frac{x}{3}) = \frac{3}{4}

General solutions for

sin (\frac{x}{3}) = \frac{3}{4}

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

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

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

Solve

\frac{x}{3} = arcsin (\frac{3}{4}) + 2 πn : x = 3 arcsin (\frac{3}{4}) + 6 πn

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

Multiply both sides by

3

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

Multiply both sides by

3

\frac{3 x}{3} = 3 arcsin (\frac{3}{4}) + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} = 3 arcsin (\frac{3}{4}) + 3 \cdot 2 πn

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

3 arcsin (\frac{3}{4}) + 3 \cdot 2 πn : 3 arcsin (\frac{3}{4}) + 6 πn

3 arcsin (\frac{3}{4}) + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 arcsin (\frac{3}{4}) + 6 πn

Solve

\frac{x}{3} = π - arcsin (\frac{3}{4}) + 2 πn : x = 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

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

Multiply both sides by

3

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

Multiply both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

3 π - 3 arcsin (\frac{3}{4}) + 3 \cdot 2 πn : 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

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

Multiply the numbers:

3 \cdot 2 = 6

= 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

x = 3 arcsin (\frac{3}{4}) + 6 πn, x = 3 π - 3 arcsin (\frac{3}{4}) + 6 πn

Show solutions in decimal form

x = 3 \cdot 0.84806 \dots + 6 πn, x = 3 π - 3 \cdot 0.84806 \dots + 6 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 4sin(x/3)-3=0 ?
The general solution for 4sin(x/3)-3=0 is x=3*0.84806…+6pin,x=3pi-3*0.84806…+6pin