Calculators - Algebra II
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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 vertex, focus, directrix, axis of symmetry, latus rectum, length of the latus rectum (focal width), focal parameter, focal length (distance), eccentricity, x-intercepts, y-intercepts, domain, and range of the entered parabola. Also, it will graph the parabola. Steps are available.
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. Also, it will graph the circle. Steps are available.
Ellipse Calculator
This calculator will find either the equation of the ellipse from the given parameters or the center, foci, vertices (major vertices), co-vertices (minor vertices), (semi)major axis length, (semi)minor axis length, area, circumference, latera recta, length of the latera recta (focal width), focal parameter, eccentricity, linear eccentricity (focal distance), directrices, x-intercepts, y-intercepts, domain, and range of the entered ellipse. Also, it will graph the ellipse. Steps are available.
Hyperbola Calculator
This calculator will find either the equation of the hyperbola from the given parameters or the center, foci, vertices, co-vertices, (semi)major axis length, (semi)minor axis length, latera recta, length of the latera recta (focal width), focal parameter, eccentricity, linear eccentricity (focal distance), directrices, asymptotes, x-intercepts, y-intercepts, domain, and range of the entered hyperbola. Also, it will graph the hyperbola. Steps are available.
Conic Section Calculator
The calculator will identify the given conic section (non-degenerate or degenerate) and find its discriminant, with steps shown. Also, it will graph the conic section.
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:
- $$$\operatorname{acot}(x)=\frac{\pi}{2}-\operatorname{atan}(x)$$$
- $$$\operatorname{acot}(x)=\operatorname{atan}\left(\frac{1}{x}\right)$$$
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 add, subract, multiply, and divide two 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 function or 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 a 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.