What is the general solution for 9arcsin(x)=3pi ?

The general solution for 9arcsin(x)=3pi is x=(sqrt(3))/2

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9arcsin(x)=3pi

9 arcsin (x) = 3 π

x = \frac{3}{2}

Solution steps

9 arcsin (x) = 3 π

Divide both sides by

9

9 arcsin (x) = 3 π

Divide both sides by

9

\frac{9 arcsin ( x )}{9} = \frac{3 π}{9}

Simplify

arcsin (x) = \frac{π}{3}

arcsin (x) = \frac{π}{3}

Apply trig inverse properties

arcsin (x) = \frac{π}{3}

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

x = sin (\frac{π}{3})

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

= \frac{3}{2}

x = \frac{3}{2}

x = \frac{3}{2}

2 sin (2 x + 10) - 3 = 0

cos (θ) = \frac{13}{6 \cdot 86}

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

tan (x) + 1 = \frac{1}{3} + \frac{1}{3} cot (x)

sin (8 x) = 1

What is the general solution for 9arcsin(x)=3pi ?
The general solution for 9arcsin(x)=3pi is x=(sqrt(3))/2