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

The general solution for 6arcsin(x)=2pi is x=(sqrt(3))/2

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6arcsin(x)=2pi

6 arcsin (x) = 2 π

x = \frac{3}{2}

Solution steps

6 arcsin (x) = 2 π

Divide both sides by

6

6 arcsin (x) = 2 π

Divide both sides by

6

\frac{6 arcsin ( x )}{6} = \frac{2 π}{6}

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}

8 cos (x) = 0

2 sin (x) \cdot tan (x) + 5 sin (x) = - 2 cos (x)

2 cot (x) sin (x) + cot (x) = 0

2 sin (x) - (2 + 3) = - 3 csc (x)

7 cos^{2} (θ) + 6 sin (θ) - 10 = - 4

What is the general solution for 6arcsin(x)=2pi ?
The general solution for 6arcsin(x)=2pi is x=(sqrt(3))/2