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Popular Trigonometry >

sin^5(3x^2+2)=0.35

Solution

sin^{5} (3 x^{2} + 2) = 0.35

Solution

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

+1

Degrees

x = 0^{\circ} + 75.63899 \dots^{\circ} n, x = 0^{\circ} - 75.63899 \dots^{\circ} n, x = 0^{\circ} + 84.20452 \dots^{\circ} n, x = 0^{\circ} - 84.20452 \dots^{\circ} n

Solution steps

sin^{5} (3 x^{2} + 2) = 0.35

For

x^{n} = f (a)

, n is odd, the solution is

x = n f (a)

sin (3 x^{2} + 2) = 5 0.35

Apply trig inverse properties

sin (3 x^{2} + 2) = 5 0.35

General solutions for

sin (3 x^{2} + 2) = 5 0.35

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Solve

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn : x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

Move

2

to the right side

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

Subtract

2

from both sides

3 x^{2} + 2 - 2 = arcsin (5 0.35) + 2 πn - 2

Simplify

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

Divide both sides by

3

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

Divide both sides by

3

\frac{3 x ^{2}}{3} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplify

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

For

x^{2} = f (a)

the solutions are

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

x = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplify

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combine the fractions

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Apply rule

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

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Simplify

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combine the fractions

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Apply rule

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

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{2 πn + arcsin ( 5 0.35 ) - 2}{3}

= - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Solve

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn : x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Move

2

to the right side

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

Subtract

2

from both sides

3 x^{2} + 2 - 2 = π - arcsin (5 0.35) + 2 πn - 2

Simplify

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

Divide both sides by

3

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

Divide both sides by

3

\frac{3 x ^{2}}{3} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplify

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

For

x^{2} = f (a)

the solutions are

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

x = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Simplify

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combine the fractions

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Apply rule

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

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Simplify

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

Combine the fractions

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3} : \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Apply rule

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

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{π + 2 πn - 2 - arcsin ( 5 0.35 )}{3}

= - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

Show solutions in decimal form

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

Graph

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