What is the general solution for 15arcsin(x)=5pi ?

The general solution for 15arcsin(x)=5pi is x=(sqrt(3))/2

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15arcsin(x)=5pi

15 arcsin (x) = 5 π

x = \frac{3}{2}

Solution steps

15 arcsin (x) = 5 π

Divide both sides by

15

15 arcsin (x) = 5 π

Divide both sides by

15

\frac{15 arcsin ( x )}{15} = \frac{5 π}{15}

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) - sin (x) = 0, 0 \leq x < 2 π

sin (x) = \frac{3}{7}

2 sin (θ) + 6 = - 3 + 6

sin (\frac{x}{2} - \frac{π}{3}) = \frac{1}{2}, 0 \leq x \leq 2 π

4 cot (x) + 1 = 0

What is the general solution for 15arcsin(x)=5pi ?
The general solution for 15arcsin(x)=5pi is x=(sqrt(3))/2