What is the general solution for 6sin(3x)+1=7 ?

The general solution for 6sin(3x)+1=7 is x= pi/6+(2pin)/3

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6sin(3x)+1=7

6 sin (3 x) + 1 = 7

x = \frac{π}{6} + \frac{2 πn}{3}

Degrees

x = 3 0^{\circ} + 12 0^{\circ} n

Solution steps

6 sin (3 x) + 1 = 7

Move

1

to the right side

6 sin (3 x) + 1 = 7

Subtract

1

from both sides

6 sin (3 x) + 1 - 1 = 7 - 1

Simplify

6 sin (3 x) = 6

6 sin (3 x) = 6

Divide both sides by

6

6 sin (3 x) = 6

Divide both sides by

6

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

Simplify

sin (3 x) = 1

sin (3 x) = 1

General solutions for

sin (3 x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

3 x = \frac{π}{2} + 2 πn

3 x = \frac{π}{2} + 2 πn

Solve

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

3 x = \frac{π}{2} + 2 πn

Divide both sides by

3

3 x = \frac{π}{2} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{6} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

sin (\frac{π}{12})

arccos (\frac{2}{2})

cos (\frac{π}{6})

sin (1 0^{\circ})

cos (x) cos (3 x) + sin (x) sin (3 x) = 0, 0 \leq x \leq 2 π

What is the general solution for 6sin(3x)+1=7 ?
The general solution for 6sin(3x)+1=7 is x= pi/6+(2pin)/3