What is the general solution for 16arcsin(x)=4pi ?

The general solution for 16arcsin(x)=4pi is x=(sqrt(2))/2

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16arcsin(x)=4pi

16 arcsin (x) = 4 π

x = \frac{2}{2}

Solution steps

16 arcsin (x) = 4 π

Divide both sides by

16

16 arcsin (x) = 4 π

Divide both sides by

16

\frac{16 arcsin ( x )}{16} = \frac{4 π}{16}

Simplify

arcsin (x) = \frac{π}{4}

arcsin (x) = \frac{π}{4}

Apply trig inverse properties

arcsin (x) = \frac{π}{4}

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

x = sin (\frac{π}{4})

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

= \frac{2}{2}

x = \frac{2}{2}

x = \frac{2}{2}

3 cos^{2} (x) - 5 cos (x) = 1 + 3 sin^{2} (x)

1 + cos (x) = 2 sin^{2} (x)

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

2 sin (3 x) + 2 = 0

0 = cos (θ)

What is the general solution for 16arcsin(x)=4pi ?
The general solution for 16arcsin(x)=4pi is x=(sqrt(2))/2