What is the general solution for solvefor x,z=arcsin^3(3x+2y) ?

The general solution for solvefor x,z=arcsin^3(3x+2y) is x=(sin(\sqrt[3]{z}))/3-(2y)/3

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solvefor x,z=arcsin^3(3x+2y)

Solution

solve for

x, z = arcsin^{3} (3 x + 2 y)

Solution

Solution steps

z = arcsin^{3} (3 x + 2 y)

Switch sides

arcsin^{3} (3 x + 2 y) = z

Solve by substitution

arcsin^{3} (3 x + 2 y) = z

Let:

arcsin (3 x + 2 y) = u

u^{3} = z

u^{3} = z

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 = arcsin (3 x + 2 y)

Apply trig inverse properties

arcsin (x) = a \Rightarrow x = sin (a)

Solve

Move

2 y

to the right side

Subtract

2 y

from both sides

Simplify

Divide both sides by

3

Divide both sides by

3

Simplify

No Solution

No Solution

No Solution

No Solution

Combine all the solutions

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cos(pi/6 t)=cos(pi/6 (t-3))

cos (\frac{π}{6} t) = cos (\frac{π}{6} (t - 3))

0=arcsin(sqrt(x))

0 = arcsin (x)

cos(2y)-sin(2y)=0

cos (2 y) - sin (2 y) = 0

Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,z=arcsin^3(3x+2y) ?
The general solution for solvefor x,z=arcsin^3(3x+2y) is x=(sin(\sqrt[3]{z}))/3-(2y)/3