What is the general solution for solvefor y,xtan(y)-x^2sin(x)+3x^3=0 ?

The general solution for solvefor y,xtan(y)-x^2sin(x)+3x^3=0 is y=arctan(x(sin(x)-3x))+pin

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Popular Trigonometry >

solvefor y,xtan(y)-x^2sin(x)+3x^3=0

Solution

solvefor

Solution

y = arctan (x (sin (x) - 3 x)) + πn

Solution steps

x tan (y) - x^{2} sin (x) + 3 x^{3} = 0

Move

x^{2} sin (x)

to the right side

x tan (y) - x^{2} sin (x) + 3 x^{3} = 0

Add

x^{2} sin (x)

to both sides

x tan (y) - x^{2} sin (x) + 3 x^{3} + x^{2} sin (x) = 0 + x^{2} sin (x)

Simplify

x tan (y) + 3 x^{3} = x^{2} sin (x)

x tan (y) + 3 x^{3} = x^{2} sin (x)

Move

3 x^{3}

to the right side

x tan (y) + 3 x^{3} = x^{2} sin (x)

Subtract

3 x^{3}

from both sides

x tan (y) + 3 x^{3} - 3 x^{3} = x^{2} sin (x) - 3 x^{3}

Simplify

x tan (y) = x^{2} sin (x) - 3 x^{3}

x tan (y) = x^{2} sin (x) - 3 x^{3}

Divide both sides by

x; x \neq = 0

x tan (y) = x^{2} sin (x) - 3 x^{3}

Divide both sides by

x; x \neq = 0

\frac{x tan ( y )}{x} = \frac{x ^{2} sin ( x )}{x} - \frac{3 x ^{3}}{x}; x \neq = 0

Simplify

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

Simplify

\frac{x tan ( y )}{x} : tan (y)

\frac{x tan ( y )}{x}

Cancel the common factor:

x

= tan (y)

Simplify

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

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

Apply rule

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

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

Factor

x^{2} sin (x) - 3 x^{3} : x^{2} (sin (x) - 3 x)

x^{2} sin (x) - 3 x^{3}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{3} = x^{2} x

= x^{2} sin (x) - 3 x^{2} x

Factor out common term

x^{2}

= x^{2} (sin (x) - 3 x)

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

Cancel the common factor:

x

= x (sin (x) - 3 x)

tan (y) = x (sin (x) - 3 x); x \neq = 0

tan (y) = x (sin (x) - 3 x); x \neq = 0

tan (y) = x (sin (x) - 3 x); x \neq = 0

Apply trig inverse properties

tan (y) = x (sin (x) - 3 x)

General solutions for

tan (y) = x (sin (x) - 3 x)

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

y = arctan (x (sin (x) - 3 x)) + πn

y = arctan (x (sin (x) - 3 x)) + πn

Graph

Popular Examples

(((1-sin^2(x)))/((1+2*sin^2(x))))=0.45

Frequently Asked Questions (FAQ)

What is the general solution for solvefor y,xtan(y)-x^2sin(x)+3x^3=0 ?
The general solution for solvefor y,xtan(y)-x^2sin(x)+3x^3=0 is y=arctan(x(sin(x)-3x))+pin