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Popular >

2sqrt(3)sin(x^2)=3

Solution

23 sin (x^{2}) = 3

Solution

x = \frac{π + 6 πn}{3}, x = - \frac{π + 6 πn}{3}, x = \frac{2 π + 6 πn}{3}, x = - \frac{2 π + 6 πn}{3}

Degrees

x = 0^{\circ} + 155.12648 \dots^{\circ} n, x = 0^{\circ} - 155.12648 \dots^{\circ} n, x = 0^{\circ} + 165.83719 \dots^{\circ} n, x = 0^{\circ} - 165.83719 \dots^{\circ} n

Solution steps

23 sin (x^{2}) = 3

Divide both sides by

23

23 sin (x^{2}) = 3

Divide both sides by

23

\frac{2 3 sin ( x ^{2} )}{2 3} = \frac{3}{2 3}

Simplify

\frac{2 3 sin ( x ^{2} )}{2 3} = \frac{3}{2 3}

Simplify

\frac{2 3 sin ( x ^{2} )}{2 3} : sin (x^{2})

\frac{2 3 sin ( x ^{2} )}{2 3}

Divide the numbers:

\frac{2}{2} = 1

= \frac{3 sin ( x ^{2} )}{3}

Cancel the common factor:

3

= sin (x^{2})

Simplify

\frac{3}{2 3} : \frac{3}{2}

\frac{3}{2 3}

Apply radical rule:

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

3 = 3^{\frac{1}{2}}

= \frac{3}{2 \cdot 3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= \frac{3 ^{1 - \frac{1}{2}}}{2}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{3 ^{\frac{1}{2}}}{2}

Apply radical rule:

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

3^{\frac{1}{2}} = 3

= \frac{3}{2}

sin (x^{2}) = \frac{3}{2}

sin (x^{2}) = \frac{3}{2}

sin (x^{2}) = \frac{3}{2}

General solutions for

sin (x^{2}) = \frac{3}{2}

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^{2} = \frac{π}{3} + 2 πn, x^{2} = \frac{2 π}{3} + 2 πn

x^{2} = \frac{π}{3} + 2 πn, x^{2} = \frac{2 π}{3} + 2 πn

Solve

x^{2} = \frac{π}{3} + 2 πn : x = \frac{π + 6 πn}{3}, x = - \frac{π + 6 πn}{3}

x^{2} = \frac{π}{3} + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{π}{3} + 2 πn, x = - \frac{π}{3} + 2 πn

Simplify

\frac{π}{3} + 2 πn : \frac{π + 6 πn}{3}

\frac{π}{3} + 2 πn

Join

\frac{π}{3} + 2 πn : \frac{π + 6 πn}{3}

\frac{π}{3} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 3}{3}

= \frac{π}{3} + \frac{2 πn \cdot 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π + 2 πn \cdot 3}{3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π + 6 πn}{3}

= \frac{π + 6 πn}{3}

Simplify

- \frac{π}{3} + 2 πn : - \frac{π + 6 πn}{3}

- \frac{π}{3} + 2 πn

Join

\frac{π}{3} + 2 πn : \frac{π + 6 πn}{3}

\frac{π}{3} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 3}{3}

= \frac{π}{3} + \frac{2 πn \cdot 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π + 2 πn \cdot 3}{3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π + 6 πn}{3}

= - \frac{π + 6 πn}{3}

x = \frac{π + 6 πn}{3}, x = - \frac{π + 6 πn}{3}

Solve

x^{2} = \frac{2 π}{3} + 2 πn : x = \frac{2 π + 6 πn}{3}, x = - \frac{2 π + 6 πn}{3}

x^{2} = \frac{2 π}{3} + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{2 π}{3} + 2 πn, x = - \frac{2 π}{3} + 2 πn

Simplify

\frac{2 π}{3} + 2 πn : \frac{2 π + 6 πn}{3}

\frac{2 π}{3} + 2 πn

Join

\frac{2 π}{3} + 2 πn : \frac{2 π + 6 πn}{3}

\frac{2 π}{3} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 3}{3}

= \frac{2 π}{3} + \frac{2 πn \cdot 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{2 π + 2 πn \cdot 3}{3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{2 π + 6 πn}{3}

= \frac{2 π + 6 πn}{3}

Simplify

- \frac{2 π}{3} + 2 πn : - \frac{2 π + 6 πn}{3}

- \frac{2 π}{3} + 2 πn

Join

\frac{2 π}{3} + 2 πn : \frac{2 π + 6 πn}{3}

\frac{2 π}{3} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 3}{3}

= \frac{2 π}{3} + \frac{2 πn \cdot 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{2 π + 2 πn \cdot 3}{3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{2 π + 6 πn}{3}

= - \frac{2 π + 6 πn}{3}

x = \frac{2 π + 6 πn}{3}, x = - \frac{2 π + 6 πn}{3}

x = \frac{π + 6 πn}{3}, x = - \frac{π + 6 πn}{3}, x = \frac{2 π + 6 πn}{3}, x = - \frac{2 π + 6 πn}{3}

Graph

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