What is the general solution for sin(3x)= 3/4 ?

The general solution for sin(3x)= 3/4 is x=(0.84806…)/3+(2pin)/3 ,x= pi/3-(0.84806…)/3+(2pin)/3

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sin(3x)= 3/4

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

x = \frac{0.84806 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.84806 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 16.19679 \dots^{\circ} + 12 0^{\circ} n, x = 43.80320 \dots^{\circ} + 12 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

3 x = arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

3

3 x = arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

Solve

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

3 x = π - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

3

3 x = π - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.84806 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.84806 \dots}{3} + \frac{2 πn}{3}

sin (x + \frac{π}{3}) + cos (x + \frac{π}{6}) = \frac{3}{3}

4 sin^{2} (x) cot (x) - 3 cot (x) = 0

sin (2 x) = - 2 cos^{2} (x)

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

1 = cot^{2} (x) + csc (x)

What is the general solution for sin(3x)= 3/4 ?
The general solution for sin(3x)= 3/4 is x=(0.84806…)/3+(2pin)/3 ,x= pi/3-(0.84806…)/3+(2pin)/3