# Calculators - Algebra II

## Partial Fraction Decomposition Calculator

This online calculator will find the partial fraction decomposition of the rational function, with steps shown.

## Factoring Calculator

The calculator will try to factor any expression (polynomial, binomial, trinomial, quadratic, rational, irrational, exponential, trigonometric, or a mix of them), with steps shown. To do this, some substitutions are first applied to convert the expression into a polynomial, and then the following techniques are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, and the rational zeros theorem.

## Polynomial Roots Calculator

The calculator will find the roots of the given polynomial and their multiplicities.

## Equation Solver

The calculator will try to find the roots (exact and numerical, real and complex), i.e. solve for $x$, $y$ or any other variable, of any equation (linear, quadratic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value) on the given interval.

## System of Equations Calculator

This solver (calculator) will try to solve a system of 2, 3, 4, 5 equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both the real and the complex solutions. To solve a system of linear equations with steps, use the system of linear equations calculator.

## Simplify Expression Calculator

This calculator will try to simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions.

## Inverse Function Calculator

The calculator will find the inverse of the given function, with steps shown. If the function is one-to-one, there will be a unique inverse.

## Parabola Calculator

This calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, eccentricity, latus rectum, length of the latus rectum, focus, vertex, directrix, focal parameter, focal length (distance), x-intercepts, y-intercepts of the entered parabola.

## Circle Calculator

This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, circumference (perimeter), area, eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle.

## Ellipse Calculator

This calculator will find either the equation of the ellipse (standard form) from the given parameters or the center, vertices, co-vertices, foci, area, circumference (perimeter), focal parameter, eccentricity, linear eccentricity, latus rectum, length of the latus rectum, directrices, (semi)major axis length, (semi)minor axis length, x-intercepts, y-intercepts, domain, and range of the entered ellipse.

To graph an ellipse, visit the ellipse graphing calculator (choose the "Implicit" option).

## Hyperbola Calculator

This calculator will find either the equation of the hyperbola (standard form) from the given parameters or the center, vertices, co-vertices, foci, asymptotes, focal parameter, eccentricity, linear eccentricity, latus rectum, length of the latus rectum, directrices, (semi)major axis length, (semi)minor axis length, x-intercepts, and y-intercepts of the entered hyperbola.

To graph a hyperbola, visit the hyperbola graphing calculator (choose the "Implicit" option).

## Midpoint Calculator

The calculator will find the midpoint for two points, with steps shown.

## Distance between Two Points Calculator

For two given points, the calculator will find the distance between them, with steps shown.

## Sine Calculator

The calculator will find the sine of the given value in radians or degrees.

The domain of the sine is $x\in \mathbb{R}$, the range is $[-1,1]$.

It is an odd function.

## Cosine Calculator

The calculator will find the cosine of the given value in radians or degrees.

The domain of the cosine is $x\in \mathbb{R}$, the range is $[-1,1]$.

It is an even function.

## Tangent Calculator

The calculator will find the tangent of the given value in radians or degrees.

The tangent $y=\tan(x)$ is such a function that $y=\frac{\sin(x)}{\cos(x)}$.

The domain of the tangent is $x \ne \frac{\pi}{2} + \pi n, n \in \mathbb{Z}$, the range is $(-\infty,\infty)$.

It is an odd function.

## Cotangent Calculator

The calculator will find the cotangent of the given value in radians or degrees.

The cotangent $y=\cot(x)$ is such a function that $y=\frac{\cos(x)}{\sin(x)}$.

The domain of the cotangent is $x \ne \pi n, n \in \mathbb{Z}$, the range is $(-\infty,\infty)$.

It is an odd function.

## Secant Calculator

The calculator will find the secant of the given value in radians or degrees.

The secant $y=\sec(x)$ is such a function that $y=\frac{1}{\cos(x)}$.

The domain of the secant is $x \ne \frac{\pi}{2} + \pi n, n \in \mathbb{Z}$, the range is $(-\infty,-1]\cup[1,\infty)$.

It is an even function.

## Cosecant Calculator

The calculator will find the cosecant of the given value in radians or degrees.

The cosecant $y=\csc(x)$ is such a function that $y=\frac{1}{\sin(x)}$.

The domain of the cosecant is $x \ne \pi n, n \in \mathbb{Z}$, the range is $(-\infty,-1]\cup[1,\infty)$.

It is an odd function.

## Inverse Sine Calculator

The calculator will find the inverse sine of the given value in radians and degrees.

The inverse sine $y=\sin^{-1}(x)$ or $y=\operatorname{asin}(x)$ or $y=\operatorname{arcsin}(x)$ is such a function that $\sin(y)=x$.

The domain of the inverse sine is $[-1,1]$, the range is $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

It is an odd function.

## Inverse Cosine Calculator

The calculator will find the inverse cosine of the given value in radians and degrees.

The inverse cosine $y=\cos^{-1}(x)$ or $y=\operatorname{acos}(x)$ or $y=\operatorname{arccos}(x)$ is such a function that $\cos(y)=x$.

The domain of the inverse cosine is $[-1,1]$, the range is $[0,\pi]$.

It is an even function.

## Inverse Tangent Calculator

The calculator will find the inverse tangent of the given value in radians and degrees.

The inverse tangent $y=\tan^{-1}(x)$ or $y=\operatorname{atan}(x)$ or $y=\operatorname{arctan}(x)$ is such a function that $\tan(y)=x$.

The domain of the inverse tangent is $(-\infty,\infty)$, the range is $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.

It is an odd function.

## Inverse Cotangent Calculator

The calculator will find the inverse cotangent of the given value in radians and degrees.

The inverse cotangent $y=\cot^{-1}(x)$ or $y=\operatorname{acot}(x)$ or $y=\operatorname{arccot}(x)$ is such a function that $\cot(y)=x$.

The domain of the inverse cotangent is $(-\infty,\infty)$, the range is $(0,\pi)$.

It is an odd function.

There are two conventional but incompatible definitions for the inverse cotangent:

1. $\operatorname{acot}(x)=\frac{\pi}{2}-\operatorname{atan}(x)$
2. $\operatorname{acot}(x)=\operatorname{atan}\left(\frac{1}{x}\right)$

We use the first definition to make the inverse cotangent continuous at $x=0$.

## Inverse Secant Calculator

The calculator will find the inverse secant of the given value in radians and degrees.

The inverse secant $y=\sec^{-1}(x)$ or $y=\operatorname{asec}(x)$ or $y=\operatorname{arcsec}(x)$ is such a function that $\sec(y)=x$.

The domain of the inverse secant is $(-\infty,-1]\cup[1,\infty)$, the range is $\left[0,\frac{\pi}{2}\right)\cup\left(\frac{\pi}{2},\pi\right]$.

This function is neither even nor odd.

## Inverse Cosecant Calculator

The calculator will find the inverse cosecant of the given value in radians and degrees.

The inverse cosecant $y=\csc^{-1}(x)$ or $y=\operatorname{acsc}(x)$ or $y=\operatorname{arccsc}(x)$ is such a function that $\csc(y)=x$.

The domain of the inverse cosecant is $(-\infty,-1]\cup[1,\infty)$, the range is $\left[-\frac{\pi}{2},0\right)\cup\left(0,\frac{\pi}{2}\right]$.

This function is neither even nor odd.

## Hyperbolic Sine Calculator

The calculator will find the hyperbolic sine of the given value.

The hyperbolic sine $y=\sinh(x)$ is such a function that $y=\frac{e^x-e^{-x}}{2}$.

The domain of the hyperbolic sine is $(-\infty,\infty)$, the range is $(-\infty,\infty)$.

It is an odd function.

## Hyperbolic Cosine Calculator

The calculator will find the hyperbolic cosine of the given value.

The hyperbolic cosine $y=\cosh(x)$ is such a function that $y=\frac{e^x+e^{-x}}{2}$.

The domain of the hyperbolic cosine is $(-\infty,\infty)$, the range is $[1,\infty)$.

It is an even function.

## Hyperbolic Tangent Calculator

The calculator will find the hyperbolic tangent of the given value.

The hyperbolic tangent $y=\tanh(x)$ is such a function that $y=\frac{\sinh(x)}{\cosh(x)}=\frac{e^x-e^{-x}}{e^x+e^{-x}}$.

The domain of the hyperbolic tangent is $(-\infty,\infty)$, the range is $(-1,1)$.

It is an odd function.

## Hyperbolic Cotangent Calculator

The calculator will find the hyperbolic cotangent of the given value.

The hyperbolic cotangent $y=\coth(x)$ is such a function that $y=\frac{\cosh(x)}{\sinh(x)}=\frac{e^x+e^{-x}}{e^x-e^{-x}}$.

The domain of the hyperbolic cotangent is $(-\infty,0)\cup(0,\infty)$, the range is $(-\infty,-1)\cup(1,\infty)$.

It is an odd function.

## Hyperbolic Secant Calculator

The calculator will find the hyperbolic secant of the given value.

The hyperbolic secant $y=\operatorname{sech}(x)$ is such a function that $y=\frac{1}{\cosh(x)}=\frac{2}{e^x+e^{-x}}$.

The domain of the hyperbolic secant is $(-\infty,\infty)$, the range is $(0,1]$.

It is an even function.

## Hyperbolic Cosecant Calculator

The calculator will find the hyperbolic cosecant of the given value.

The hyperbolic cosecant $y=\operatorname{csch}(x)$ is such a function that $y=\frac{1}{\sinh(x)}=\frac{2}{e^x-e^{-x}}$.

The domain of the hyperbolic cosecant is $(-\infty,0)\cup(0,\infty)$, the range is $(-\infty,0)\cup(0,\infty)$.

It is an odd function.

## Inverse Hyperbolic Sine Calculator

The calculator will find the inverse hyperbolic sine of the given value.

The inverse hyperbolic sine $y=\sinh^{-1}(x)$ or $y=\operatorname{asinh}(x)$ or $y=\operatorname{arcsinh}(x)$ is such a function that $\sinh(y)=x$.

It can be expressed in terms of elementary functions: $y=\sinh^{-1}(x)=\ln\left(x+\sqrt{x^2+1}\right)$.

The domain of the inverse hyperbolic sine is $(-\infty,\infty)$, the range is $(-\infty,\infty)$.

It is an odd function.

## Inverse Hyperbolic Cosine Calculator

The calculator will find the inverse hyperbolic cosine of the given value.

The inverse hyperbolic cosine $y=\cosh^{-1}(x)$ or $y=\operatorname{acosh}(x)$ or $y=\operatorname{arccosh}(x)$ is such a function that $\cosh(y)=x$.

It can be expressed in terms of elementary functions: $y=\cosh^{-1}(x)=\ln\left(x+\sqrt{x^2-1}\right)$.

The domain of the inverse hyperbolic cosine is $[1,\infty)$, the range is $[0,\infty)$.

This function is neither even nor odd.

## Inverse Hyperbolic Tangent Calculator

The calculator will find the inverse hyperbolic tangent of the given value.

The inverse hyperbolic tangent $y=\tanh^{-1}(x)$ or $y=\operatorname{atanh}(x)$ or $y=\operatorname{arctanh}(x)$ is such a function that $\tanh(y)=x$.

It can be expressed in terms of elementary functions: $y=\tanh^{-1}(x)=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)$.

The domain of the inverse hyperbolic tangent is $(-1,1)$, the range is $(-\infty,\infty)$.

It is an odd function.

## Inverse Hyperbolic Cotangent Calculator

The calculator will find the inverse hyperbolic cotangent of the given value.

The inverse hyperbolic cotangent $y=\coth^{-1}(x)$ or $y=\operatorname{acoth}(x)$ or $y=\operatorname{arccoth}(x)$ is such a function that $\coth(y)=x$.

It can be expressed in terms of elementary functions: $y=\coth^{-1}(x)=\frac{1}{2}\ln\left(\frac{x+1}{x-1}\right)$.

The domain of the inverse hyperbolic cotangent is $(-\infty,-1)\cup(1,\infty)$, the range is $(-\infty,0)\cup(0,\infty)$.

It is an odd function.

## Inverse Hyperbolic Secant Calculator

The calculator will find the inverse hyperbolic secant of the given value.

The inverse hyperbolic secant $y=\operatorname{sech}^{-1}(x)$ or $y=\operatorname{asech}(x)$ or $y=\operatorname{arcsech}(x)$ is such a function that $\operatorname{sech}(y)=x$.

It can be expressed in terms of elementary functions: $y=\operatorname{sech}^{-1}(x)=\ln\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)$.

The domain of the inverse hyperbolic secant is $(0,1]$, the range is $[0,\infty)$.

This function is neither even nor odd.

## Inverse Hyperbolic Cosecant Calculator

The calculator will find the inverse hyperbolic cosecant of the given value.

The inverse hyperbolic cosecant $y=\operatorname{csch}^{-1}(x)$ or $y=\operatorname{acsch}(x)$ or $y=\operatorname{arccsch}(x)$ is such a function that $\operatorname{csch}(y)=x$.

It can be expressed in terms of elementary functions: $y=\operatorname{csch}^{-1}(x)=\ln\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}+1}\right)$.

The domain of the inverse hyperbolic cosecant is $(-\infty,0)\cup(0,\infty)$, the range is $(-\infty,0)\cup(0,\infty)$.

It is an odd function.

## Rotation Calculator

The calculator will rotate the given point around another given point (counterclockwise or clockwise), with steps shown.

## Binomial Expansion Calculator

The calculator will find the binomial expansion of the given expression, with steps shown.

## Logarithm Calculator

The calculator will find the logarithm (natural, decimal, etc.) of the given value to the given base ($e$, $10$, etc.).

The domain of the logarithm is $(0,\infty)$, the range is $(-\infty,\infty)$.

It is neither an even nor an odd function.

If you enter a value outside of the domain, the result will be a complex number.

If you enter a negative base, the result will be a complex number.

## Inequality Calculator

This calculator will try to solve the linear, quadratic, polynomial, rational, and absolute value inequalities. It can handle compound inequalities and systems of inequalities as well.

To graph inequalities, use the graphing calculator.

## Operations on Functions Calculator

The calculator will find the sum $(f+g)(x)$, difference $(f-g)(x)$, product $(fg)(x)$, and quotient $\left(\frac{f}{g}\right)(x)$ of the functions $f(x)$ and $g(x)$, with steps shown. It will also evaluate the resulting functions at the specified point if needed.

## Composite Function Calculator

The calculator will find the compositions $(f\circ g)(x)$, $(g\circ f)(x)$, $(f\circ f)(x)$, and $(f\circ g)(x)$ of the functions $f(x)$ and $g(x)$, with steps shown. It will also evaluate the compositions at the specified point if needed.

## Evaluate Calculator

The calculator will find the value of the given expression, plugging the values of the given variables if needed.

## Solve for X Calculator

The calculator will try to find the $x$ (exact and numerical, real and complex) in the given equation.

## Zeros Calculator

The calculator will try to find the zeros (exact and numerical, real and complex) of the linear, quadratic, cubic, quartic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, and absolute value function on the given interval.

## Simultaneous Equations Solver

This calculator will try to solve the system of 2, 3, 4, 5 simultaneous equations of any kind, including the polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both the real and the complex solutions.

## Trigonometry Calculator

This calculator can solve trigonometric equations, simplify and evaluate expressions. It can handle trigonometric and inverse trigonometric functions.

## Polar Form of a Complex Number Calculator

The calculator will find the polar form of the given complex number, with steps shown.

## Complex Number Calculator

The calculator will try to simplify any complex expression, with steps shown. It will perform addition, subtraction, multiplication, division, raising to power, and also will find the polar form, conjugate, modulus, and inverse of the complex number.

## Intercepts Calculator

The calculator will try to find the x- and y-intercepts of the given function, expression, or equation.

## Roots of Complex Number Calculator

The calculator will find the $n$-th roots of the given complex number using de Moivre's formula, with steps shown.

## Cubic Equation Calculator

The calculator will find the roots of the cubic equation in both the analytic and the approximate forms.

## Quartic Equation Calculator

The calculator will find the roots of the quartic equation in both the analytic and the approximate forms.

## Exponential Function Calculator

This calculator will calculate the exponential function with the given base and exponent.

## Cramer's Rule Calculator

This calculator will solve the system of linear equations of any kind, with steps shown, using Cramer's rule.

## System of Linear Equations Calculator

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan elimination method, the inverse matrix method, or Cramer's rule.

## End Behavior Calculator

This calculator will determine the end behavior of the given polynomial function, with steps shown.

## Degree and Leading Coefficient Calculator

The calculator will find the degree, leading coefficient, and leading term of the given polynomial function.

## Factorial Calculator

The calculator will find the factorial of the given number (integer or non-integer, negative or non-negative), with steps shown.