What is the general solution for sin(2x)= pi/6 ?

The general solution for sin(2x)= pi/6 is x=(0.55106…)/2+pin,x= pi/2-(0.55106…)/2+pin

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sin(2x)= pi/6

sin (2 x) = \frac{π}{6}

x = \frac{0.55106 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.55106 \dots}{2} + πn

Degrees

x = 15.78698 \dots^{\circ} + 18 0^{\circ} n, x = 74.21301 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = \frac{π}{6}

Apply trig inverse properties

sin (2 x) = \frac{π}{6}

General solutions for

sin (2 x) = \frac{π}{6}

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

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

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

Solve

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

2 x = arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

2 x = π - arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{π}{6}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.55106 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.55106 \dots}{2} + πn

sin (x) = \frac{8}{17} sin (2 x)

2 = 1 + sin (2 x)

cosh (x - 1) = 2

tan (x) = \frac{7}{25}

tan (x) = - 1, 0 < x < 2 π

What is the general solution for sin(2x)= pi/6 ?
The general solution for sin(2x)= pi/6 is x=(0.55106…)/2+pin,x= pi/2-(0.55106…)/2+pin