What is the general solution for solvefor x,tan^3(x)=f ?

The general solution for solvefor x,tan^3(x)=f is x=arctan(\sqrt[3]{f})+pin

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solvefor x,tan^3(x)=f

Solution

solve for

x, tan^{3} (x) = f

Solution

Solution steps

tan^{3} (x) = f

Solve by substitution

tan^{3} (x) = f

Let:

tan (x) = u

u^{3} = f

u^{3} = 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 = tan (x)

Apply trig inverse properties

General solutions for

tan (x) = a \Rightarrow x = arctan (a) + πn

No Solution

No Solution

No Solution

No Solution

Combine all the solutions

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solvefor y,3tan(y)-4= 2/5 solve for

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4-3sin(θ)=7

4 - 3 sin (θ) = 7

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sin (x) cos (x) = - \frac{1}{4}, 0 \leq x \leq 2 π

tan(x)=(4/3)

tan (x) = (\frac{4}{3})

Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,tan^3(x)=f ?
The general solution for solvefor x,tan^3(x)=f is x=arctan(\sqrt[3]{f})+pin