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

The general solution for arcsin(x)= pi/6 is x= 1/2

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arcsin(x)= pi/6

arcsin (x) = \frac{π}{6}

x = \frac{1}{2}

Solution steps

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}

2 sin^{2} (θ) = 3 (cos (θ) + 1)

sin (θ) = 0.3

tan (\frac{x}{2}) + 3 = 0

tan^{2} (θ) - 4 = 0

csc^{2} (θ) - 2 csc (θ) - 8 = 0

What is the general solution for arcsin(x)= pi/6 ?
The general solution for arcsin(x)= pi/6 is x= 1/2