What is the general solution for 5sin(3x)-1=3 ?

The general solution for 5sin(3x)-1=3 is x=(0.92729…)/3+(2pin)/3 ,x= pi/3-(0.92729…)/3+(2pin)/3

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5sin(3x)-1=3

5 sin (3 x) - 1 = 3

x = \frac{0.92729 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 17.71003 \dots^{\circ} + 12 0^{\circ} n, x = 42.28996 \dots^{\circ} + 12 0^{\circ} n

Solution steps

5 sin (3 x) - 1 = 3

Move

1

to the right side

5 sin (3 x) - 1 = 3

Add

1

to both sides

5 sin (3 x) - 1 + 1 = 3 + 1

Simplify

5 sin (3 x) = 4

5 sin (3 x) = 4

Divide both sides by

5

5 sin (3 x) = 4

Divide both sides by

5

\frac{5 sin ( 3 x )}{5} = \frac{4}{5}

Simplify

sin (3 x) = \frac{4}{5}

sin (3 x) = \frac{4}{5}

Apply trig inverse properties

sin (3 x) = \frac{4}{5}

General solutions for

sin (3 x) = \frac{4}{5}

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

3 x = arcsin (\frac{4}{5}) + 2 πn, 3 x = π - arcsin (\frac{4}{5}) + 2 πn

3 x = arcsin (\frac{4}{5}) + 2 πn, 3 x = π - arcsin (\frac{4}{5}) + 2 πn

Solve

3 x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

3

3 x = arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

Solve

3 x = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

3

3 x = π - arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{0.92729 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{3} + \frac{2 πn}{3}

- 5 sin (x) = 0

sin^{2} (θ) = 6 (cos (- θ) + 1)

5 sin (θ) - 2 = 0

(2 cos (x) - 2) (2 sin (x) - 2) = 0

- 4 cos (5 x) + 1 = 1

What is the general solution for 5sin(3x)-1=3 ?
The general solution for 5sin(3x)-1=3 is x=(0.92729…)/3+(2pin)/3 ,x= pi/3-(0.92729…)/3+(2pin)/3