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

The general solution for 3arcsin(x)= pi/2 ,x is No Solution for x\in\mathbb{R}

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3arcsin(x)= pi/2 ,x

3 arcsin (x) = \frac{π}{2}, x

No Solution for x \in R

Solution steps

3 arcsin (x) = \frac{π}{2}, x

Divide both sides by

3

3 arcsin (x) = \frac{π}{2}

Divide both sides by

3

\frac{3 arcsin ( x )}{3} = \frac{\frac{π}{2}}{3}

Simplify

\frac{3 arcsin ( x )}{3} = \frac{\frac{π}{2}}{3}

Simplify

\frac{3 arcsin ( x )}{3} : arcsin (x)

\frac{3 arcsin ( x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= arcsin (x)

Simplify

\frac{\frac{π}{2}}{3} : \frac{π}{6}

\frac{\frac{π}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π}{6}

arcsin (x) = \frac{π}{6}

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}

Solutions for the range

x

No Solution for x \in R

sin^{2} (θ) - \frac{1}{2} sin (θ) - \frac{1}{2} = 0

tan^{2} (x) - sec (x) + 1 = 0

sin (2 y) = 0

7 sin^{2} (θ) - 15 sin (θ) + 8 = 0

sin (5 t) = 0

What is the general solution for 3arcsin(x)= pi/2 ,x ?
The general solution for 3arcsin(x)= pi/2 ,x is No Solution for x\in\mathbb{R}