What is the general solution for sqrt(1-sin(x))=0 ?

The general solution for sqrt(1-sin(x))=0 is x= pi/2+2pin

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sqrt(1-sin(x))=0

Solution

1 - sin (x) = 0

Solution

x = \frac{π}{2} + 2 πn

Solution steps

1 - sin (x) = 0

Square both sides:

1 - sin (x) = 0

1 - sin (x) = 0

(1 - sin (x))^{2} = 0^{2}

Expand

(1 - sin (x))^{2} : 1 - sin (x)

(1 - sin (x))^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

= (1 - sin (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

= 1 - sin (x)

Expand

0^{2} : 0

0^{2}

Apply rule

0^{a} = 0

= 0

1 - sin (x) = 0

1 - sin (x) = 0

Solve

1 - sin (x) = 0 : sin (x) = 1

1 - sin (x) = 0

Move

1

to the right side

1 - sin (x) = 0

Subtract

1

from both sides

1 - sin (x) - 1 = 0 - 1

Simplify

- sin (x) = - 1

- sin (x) = - 1

Divide both sides by

- 1

- sin (x) = - 1

Divide both sides by

- 1

\frac{- sin ( x )}{- 1} = \frac{- 1}{- 1}

Simplify

sin (x) = 1

sin (x) = 1

sin (x) = 1

Verify Solutions:

sin (x) = 1

True

Check the solutions by plugging them into

1 - sin (x) = 0

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

Plug in

sin (x) = 1 :

True

1 - 1 = 0

1 - 1 = 0

1 - 1

Subtract the numbers:

1 - 1 = 0

= 0

Apply rule

0 = 0

= 0

0 = 0

True

The solution is

sin (x) = 1

General solutions for

sin (x) = 1

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}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for sqrt(1-sin(x))=0 ?
The general solution for sqrt(1-sin(x))=0 is x= pi/2+2pin