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

The general solution for -3sin(3x)=1 is x=-(0.33983…)/3+(2pin)/3 ,x= pi/3+(0.33983…)/3+(2pin)/3

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-3sin(3x)=1

- 3 sin (3 x) = 1

x = - \frac{0.33983 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.33983 \dots}{3} + \frac{2 πn}{3}

Degrees

x = - 6.49040 \dots^{\circ} + 12 0^{\circ} n, x = 66.49040 \dots^{\circ} + 12 0^{\circ} n

Solution steps

- 3 sin (3 x) = 1

Divide both sides by

- 3

- 3 sin (3 x) = 1

Divide both sides by

- 3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

3 x = arcsin (- \frac{1}{3}) + 2 πn

Simplify

arcsin (- \frac{1}{3}) + 2 πn : - arcsin (\frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 2 πn

3 x = - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

3

3 x = - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

Solve

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

3 x = π + arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

3

3 x = π + arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{0.33983 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.33983 \dots}{3} + \frac{2 πn}{3}

\frac{1}{cos ( x ) - cos ( x )} = sin (x) tan (x)

cos (θ) = \frac{3}{5} (270360)

2 sin (x) = tan (x) cos (x) - cos (x)

x, z = 3 - sin (2 x + y)

tan (x) = \frac{27}{48}

What is the general solution for -3sin(3x)=1 ?
The general solution for -3sin(3x)=1 is x=-(0.33983…)/3+(2pin)/3 ,x= pi/3+(0.33983…)/3+(2pin)/3