What is the general solution for 18arcsin(x)=3pi ?

The general solution for 18arcsin(x)=3pi is x= 1/2

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18arcsin(x)=3pi

18 arcsin (x) = 3 π

x = \frac{1}{2}

Solution steps

18 arcsin (x) = 3 π

Divide both sides by

18

18 arcsin (x) = 3 π

Divide both sides by

18

\frac{18 arcsin ( x )}{18} = \frac{3 π}{18}

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}

(2 cos (x) - 3) (2 sin (x) - 1) = 0

11 tan (θ) - 10 = 4 tan (θ) - 4

sec^{2} (x) - 8 sec (x) = 0

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

7 tan (A) + 42 = 0

What is the general solution for 18arcsin(x)=3pi ?
The general solution for 18arcsin(x)=3pi is x= 1/2