What is the general solution for 0=arcsin(sqrt(x)) ?

The general solution for 0=arcsin(sqrt(x)) is x=0

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Popular >

0=arcsin(sqrt(x))

Solution

0 = arcsin (x)

Solution

x = 0

Solution steps

0 = arcsin (x)

Switch sides

arcsin (x) = 0

Apply trig inverse properties

arcsin (x) = 0

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

x = sin (0)

sin (0) = 0

sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

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}

= 0

= 0

x = 0

x = 0

Solve

x = 0 : x = 0

x = 0

Square both sides:

x = 0

x = 0

(x)^{2} = 0^{2}

Expand

(x)^{2} : x

(x)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (x^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= x^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= x

Expand

0^{2} : 0

0^{2}

Apply rule

0^{a} = 0

= 0

x = 0

x = 0

Verify Solutions:

x = 0

True

Check the solutions by plugging them into

x = 0

Remove the ones that don't agree with the equation.

Plug in

x = 0 :

True

0 = 0

0 = 0

0

Apply rule

0 = 0

= 0

0 = 0

True

The solution is

x = 0

x = 0

Popular Examples

cos(2y)-sin(2y)=0

cos (2 y) - sin (2 y) = 0

sec((2pi)/3+x)=2

sec (\frac{2 π}{3} + x) = 2

sin(t)= 7/9 ,sin(2t)

sin (t) = \frac{7}{9}, sin (2 t)

8/17 =sin(2x)

\frac{8}{17} = sin (2 x)

sec(2x)+tan(2x)=2

sec (2 x) + tan (2 x) = 2

Frequently Asked Questions (FAQ)

What is the general solution for 0=arcsin(sqrt(x)) ?
The general solution for 0=arcsin(sqrt(x)) is x=0