What is the general solution for 6sin(3x)=5 ?

The general solution for 6sin(3x)=5 is x=(0.98511…)/3+(2pin)/3 ,x= pi/3-(0.98511…)/3+(2pin)/3

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6sin(3x)=5

6 sin (3 x) = 5

x = \frac{0.98511 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.98511 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 18.81423 \dots^{\circ} + 12 0^{\circ} n, x = 41.18576 \dots^{\circ} + 12 0^{\circ} n

Solution steps

6 sin (3 x) = 5

Divide both sides by

6

6 sin (3 x) = 5

Divide both sides by

6

\frac{6 sin ( 3 x )}{6} = \frac{5}{6}

Simplify

sin (3 x) = \frac{5}{6}

sin (3 x) = \frac{5}{6}

Apply trig inverse properties

sin (3 x) = \frac{5}{6}

General solutions for

sin (3 x) = \frac{5}{6}

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

3 x = arcsin (\frac{5}{6}) + 2 πn, 3 x = π - arcsin (\frac{5}{6}) + 2 πn

3 x = arcsin (\frac{5}{6}) + 2 πn, 3 x = π - arcsin (\frac{5}{6}) + 2 πn

Solve

3 x = arcsin (\frac{5}{6}) + 2 πn : x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{5}{6}) + 2 πn

Divide both sides by

3

3 x = arcsin (\frac{5}{6}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

Solve

3 x = π - arcsin (\frac{5}{6}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{5}{6}) + 2 πn

Divide both sides by

3

3 x = π - arcsin (\frac{5}{6}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{0.98511 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.98511 \dots}{3} + \frac{2 πn}{3}

x, 4 sin^{2} (x) = 5 - 4 cos (x)

3 (sin (x)) = (3) (cos (x))

sin (a) = 12500

\frac{4}{3} = tan (θ)

cos^{2} (2 x) = \frac{1 + cos ( 2 x )}{2}

What is the general solution for 6sin(3x)=5 ?
The general solution for 6sin(3x)=5 is x=(0.98511…)/3+(2pin)/3 ,x= pi/3-(0.98511…)/3+(2pin)/3