What is the general solution for 12arcsin(x)=2pi ?

The general solution for 12arcsin(x)=2pi is x= 1/2

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12arcsin(x)=2pi

12 arcsin (x) = 2 π

x = \frac{1}{2}

Solution steps

12 arcsin (x) = 2 π

Divide both sides by

12

12 arcsin (x) = 2 π

Divide both sides by

12

\frac{12 arcsin ( x )}{12} = \frac{2 π}{12}

Simplify

arcsin (x) = \frac{π}{6}

arcsin (x) = \frac{π}{6}

Apply trig inverse properties

arcsin (x) = \frac{π}{6}

arcsin (x) = a \Rightarrow x = sin (a)

x = sin (\frac{π}{6})

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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}

= \frac{1}{2}

= \frac{1}{2}

x = \frac{1}{2}

x = \frac{1}{2}

csc (x) = - 1 - cot (x)

cos (2 θ) + 5 cos (θ) + 3 = 0

2 cos (x) = 2

sin (2 θ) = 3 sin (θ)

cot (\frac{x}{2}) = 1

What is the general solution for 12arcsin(x)=2pi ?
The general solution for 12arcsin(x)=2pi is x= 1/2