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Popular >

solvefor x,b*f=sin^3(x)

Solution

solve for

x, b \cdot f = sin^{3} (x)

Solution

Solution steps

b f = sin^{3} (x)

Switch sides

sin^{3} (x) = b f

Solve by substitution

sin^{3} (x) = b f

Let:

sin (x) = u

u^{3} = b f

u^{3} = b f

For

x^{3} = f (a)

the solutions are

Simplify

Rewrite

in standard complex form:

Multiply fractions:

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

Expand

Apply the distributive law:

a (b + c) = ab + a c

Apply minus-plus rules

+ (- a) = - a

Multiply:

Apply the fraction rule:

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

Simplify

Rewrite

in standard complex form:

Multiply fractions:

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

Expand

Apply the distributive law:

a (b - c) = ab - a c

Apply minus-plus rules

+ (- a) = - a

Multiply:

Apply the fraction rule:

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

Substitute back

u = sin (x)

Apply trig inverse properties

General solutions for

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

No Solution

No Solution

No Solution

No Solution

Combine all the solutions

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