What is the general solution for 4sin(3x)-1=0 ?

The general solution for 4sin(3x)-1=0 is x=(0.25268…)/3+(2pin)/3 ,x= pi/3-(0.25268…)/3+(2pin)/3

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4sin(3x)-1=0

4 sin (3 x) - 1 = 0

x = \frac{0.25268 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.25268 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 4.82583 \dots^{\circ} + 12 0^{\circ} n, x = 55.17416 \dots^{\circ} + 12 0^{\circ} n

Solution steps

4 sin (3 x) - 1 = 0

Move

1

to the right side

4 sin (3 x) - 1 = 0

Add

1

to both sides

4 sin (3 x) - 1 + 1 = 0 + 1

Simplify

4 sin (3 x) = 1

4 sin (3 x) = 1

Divide both sides by

4

4 sin (3 x) = 1

Divide both sides by

4

\frac{4 sin ( 3 x )}{4} = \frac{1}{4}

Simplify

sin (3 x) = \frac{1}{4}

sin (3 x) = \frac{1}{4}

Apply trig inverse properties

sin (3 x) = \frac{1}{4}

General solutions for

sin (3 x) = \frac{1}{4}

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

3 x = arcsin (\frac{1}{4}) + 2 πn, 3 x = π - arcsin (\frac{1}{4}) + 2 πn

3 x = arcsin (\frac{1}{4}) + 2 πn, 3 x = π - arcsin (\frac{1}{4}) + 2 πn

Solve

3 x = arcsin (\frac{1}{4}) + 2 πn : x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

3

3 x = arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Solve

3 x = π - arcsin (\frac{1}{4}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

3

3 x = π - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{0.25268 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.25268 \dots}{3} + \frac{2 πn}{3}

\frac{7}{4} cos (3 θ) - 1 = 0

cos (x) = sin (\frac{7 π}{6}), 0 \leq x \leq 2 π

cos (2 x) = \frac{( 3 k - 3 )}{8}

1.5 = 2.75 cos (30 (x - 4)) + 3.25

sin (x) = (\frac{5}{12})

What is the general solution for 4sin(3x)-1=0 ?
The general solution for 4sin(3x)-1=0 is x=(0.25268…)/3+(2pin)/3 ,x= pi/3-(0.25268…)/3+(2pin)/3