What is the general solution for pi/6 =sin(3x) ?

The general solution for pi/6 =sin(3x) is x=(0.55106…)/3+(2pin)/3 ,x= pi/3-(0.55106…)/3+(2pin)/3

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pi/6 =sin(3x)

\frac{π}{6} = sin (3 x)

x = \frac{0.55106 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.55106 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 10.52465 \dots^{\circ} + 12 0^{\circ} n, x = 49.47534 \dots^{\circ} + 12 0^{\circ} n

Solution steps

\frac{π}{6} = sin (3 x)

Switch sides

sin (3 x) = \frac{π}{6}

Apply trig inverse properties

sin (3 x) = \frac{π}{6}

General solutions for

sin (3 x) = \frac{π}{6}

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

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

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

Solve

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

3 x = arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

3

3 x = arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

Solve

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

3 x = π - arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

3

3 x = π - arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.55106 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.55106 \dots}{3} + \frac{2 πn}{3}

tan (x) = 3 tan (\frac{1}{2} x)

cos (t) = \frac{- 5}{13}, \frac{1}{2} π < t < π

31.91 cos (x) = 20.48

7 sin (x) + 7 sin (x) tan (x) = 0

0 = cos (20 t) - cos (20.02 t)

What is the general solution for pi/6 =sin(3x) ?
The general solution for pi/6 =sin(3x) is x=(0.55106…)/3+(2pin)/3 ,x= pi/3-(0.55106…)/3+(2pin)/3