Trig Functions
Function | Try typing... | This function plots or finds the... |
---|---|---|
sine | sin\((x)\) | sine of an angle |
cosine | cos\((x)\) | cosine of an angle |
tangent | tan\((x)\) | tangent of an angle |
cosecant | csc\((x)\) | cosecant of an angle |
secant | sec\((x\)) | secant of an angle |
cotangent | cot\((x\)) | cotangent of an angle |
Inverse Trig Functions
Function | Try typing... | This function plots or finds the... |
---|---|---|
arcsine | sin\(^{-1}(x)\) | inverse of the sine of an angle |
arccosine | cos\(^{-1}(x)\) | inverse of the cosine of an angle |
arctangent | tan\(^{-1}(x\)) | inverse of the tangent of an angle |
arccosecant | csc\(^{-1}(x\)) | inverse of the cosecant of an angle |
arcsecant | sec\(^{-1}(x\)) | inverse of the secant of an angle |
arccotangent | cot\(^{-1}(x\)) | inverse of the cotangent of an angle |
Statistics
Function | Try typing... | This function finds the... |
---|---|---|
mean | mean\(([1,5,5,10])\) | average of a list of numbers |
median | median\(([1,5,5,10])\) | middle value of a list of numbers |
minimum | min\(([1,5,5,10])\) | minimum value of a list of numbers |
maximum | max\(([1,5,5,10])\) | maximum value of a list of numbers |
quartile | quartile\(([1,5,5,10],4)\) | qth quartile of a list of numbers (list,q) (q must be a number between 0 and 4 (inclusive)) |
quantile | quantile\(([1,5,5,10],4)\) | qth quantile of a list of numbers (list,q) (q must be a number between 0 and 1 (inclusive)) |
standard deviation | stdev\(([1,5,5,10])\) | sample standard deviation of a list of numbers |
standard deviation population | stdevp\(([1,5,5,10])\) | population standard deviation of a list of numbers |
variance | var\(([1,5,5,10])\) | sample variance of a list of numbers |
population variance | varp\(([1,5,5,10])\) | population variance of a list of numbers |
mean absolute deviation | mad\(([1,5,5,10])\) | mean absolute deviation of a list of numbers |
covariance | cov\((l_{1},l_2)\) | sample covariance between two list of numbers |
population covariance | covp\((l_{1},l_2)\) | population covariance between two list of numbers |
Pearson correlation coefficient | corr\((l_{1},l_2)\) | Pearson correlation coefficient between two list of numbers |
Spearman | spearman\((l_{1},l_2)\) | Spearman's rank correlation coefficient between two lists of numbers |
stats | stats\(([2,3,3,5,6,7,8])\) | five number summary - (minimum, first quartile, median, third quartile, and maximum values) of a list |
count | count\(([1,5,5,10])\) | number of elements in a list |
total | total\(([1,5,5,10])\) | sum of a list |
List Operations
Function | Try typing... | This function... |
---|---|---|
join | join\((l_{1},l_2)\) | joins multiple lists into one |
sort | sort\(([5,1,5,10])\) | sorts the elements in a list |
shuffle | shuffle\(([1,5,5,10])\) | shuffles the elements in a list |
unique | unique\(([1,5,5,10])\) | makes a list of the unique elements of an original list |
for | (a,a) for \(1 \lt a \lt 3\) | plots points or evaluates a variable for multiple values in a list or graphs a continuous curve for a finite or infinite interval |
Visualizations
Function | Try typing... | This function plots a... |
---|---|---|
histogram | histogram\(([1,5,5,10])\) | histogram from the data contained in list using bin width to group the data. (The bin width may be optionally passed in as a second argument. If not, it defaults to 1). |
dotplot | dotplot\(([1,5,5,10])\) | dot plot from the data contained in list using bin width to group the data. (The bin width may be optionally passed in as a second argument. If not, it defaults to 1). |
boxplot | boxplot\(([1,5,5,10])\) | box-and-whisker plot from the data contained in list |
Distributions
Function | Try typing... | This function plots the... |
---|---|---|
normal distribution | normaldist\((0,1)\) | probability density function (PDF) of a normal distribution with the given mean and standard deviation |
t-distribution | tdist\((10)\) | probability density function (PDF) of a t-distribution with the given degrees of freedom |
poisson distribution | poissondist\((5.5)\) | probability mass function (PMF) of a Poisson distribution with the given mean |
binomial distribution | binomialdist\((10,0.3)\) | probability mass function (PMF) of a binomial distribution given a number of (independent) trials and a probability of success on each trial |
uniform distribution | uniformdist\((0,1)\) | probability density function (PDF) of a uniform distribution with the given minimum and maximum |
probability density function | pdf\((D,x)\) | probability density function (PDF) of the normal distribution \((D)\) |
cumulative distribution function | cdf\((D,x)\) | cumulative distribution function (CDF) of the normal distribution \((D)\) |
inverse cumulative density function | inversecdf\((C,x)\) | inverse cumulative distribution function (CDF) of the normal distribution \((D)\) |
random | random\(( )\) | random\(( )\) chooses a random number in the interval \([0,1)\), random\((l_1)\) will choose one random number from the list |
Statistical Tests
Function | Try typing... | This function... |
---|---|---|
t-test | ttest\(([85,90,78,92,88], 80)\) | performs a one-sample t-test to compare the mean of a list of data to a hypothesized mean |
t-score | tscore\(([85,90,78,92,88], 80)\) | finds the number of standard deviations that the mean of a list of data is away from the hypothesized mean |
independent two-sample t-test | ittest\((l_{1},l_2)\) | performs an independent (unpaired) two-sample t-test to compare the mean of list1 to the mean of list2 |
Calculus
Function | Try typing... | This function plots the... |
---|---|---|
exponential | exp\((x)\) | exponential function of \(x\) |
natural logarithm | ln\((x)\) | natural log of \(x\) |
logarithm | log\((x)\) | logarithm of \(x\) |
logarithm with base a | log\(_{a}(x)\) | logarithm of \(x\) given a base value |
derivative as d/dx | \(d/dx\) | derivative with respect to \(x\) |
derivative using prime notation | \(f’(x)\) | derivative of the function \(f(x)\) |
integral | int | calculates the total value of a function over an interval (the upper and lower bound) |
summation | sum | calculate the sum of a sequence from the lower limit of the index to the upper limit of the index |
product | prod | calculate the product of a sequence of factors from the lower limit of the index to the upper limit of the index |
Hyperbolic Trig Functions
Function | Try typing... | This function plots or finds the... |
---|---|---|
hyperbolic sine | sinh\((x)\) | hyperbolic sine of an angle |
hyperbolic cosine | cosh\((x)\) | hyperbolic cosine of an angle |
hyperbolic tangent | tanh\((x)\) | hyperbolic tangent of an angle |
hyperbolic cosecant | csch\((x)\) | hyperbolic cosecant of an angle |
hyperbolic secant | sech\((x)\) | hyperbolic secant of an angle |
hyperbolic cotangent | coth\((x)\) | hyperbolic cotangent of an angle |
Custom Colors
Function | Try typing... | Define a custom color by providing... |
---|---|---|
rgb | \(c=\)rgb\((255, 165, 0)\) | the amount of red, green, and blue as values between 0 and 255 |
hsv | \(c=\)hsv\((25,0.8,1)\) | the hue (a value between 0 and 360), saturation (a value between 0 and 1), and brightness (a value between 0 and 1) |
Sound
Function | Try typing... | Description |
---|---|---|
tone | tone\((440)\) | make a sound by providing a frequency input from 110 to 880 and an optional gain input from 0 to 1 |
Number Theory
Function | Try typing... | This function finds the… |
---|---|---|
least common multiple | lcm\((2,3,4)\) | least common multiple of two or more numbers |
greatest common divisor | gcd\((6,12,18)\) | greatest common divisor of two or more numbers |
modulo | mod\((17,5)\) | remainder value after division by the divisor (modulus) |
least integer | ceil\((13.5)\) | least integer greater than or equal to a number |
greatest integer | floor\((13.5)\) | greatest integer less than or equal to a number |
round | round\((1.3254, 2)\) | value rounded to the nearest integer or given place value |
sign | sign\((-20)\) | sign of a number as positive 1 or negative 1 |
nth root | nthroot | the nth root of a number |
permutation | nPr\((6,2)\) | the number of ways to arrange \(r\) objects from a set of \(n\) distinct objects (the order of the objects matters) |
combination | nCr\((6,2)\) | the number of ways to choose \(r\) objects from a set of \(n\) distinct objects (the order of the objects does not matter) |
Advanced
Function | Try typing... | Description |
---|---|---|
action(\(\to\)) | \(a \to a+1\) | updates the variable when the action runs |
with | \(\frac{m}{n} + m\) with \(m = 10, n = 2\) | replace a variable in an expression with a constant value, another variable expression, or a list |
Geometry
Function | Try typing... | Arguments | Description |
---|---|---|---|
midpoint | midpoint\(((0,2),(4,5))\) | segment or two points | point equidistant between 2 points |
distance | distance\(((0,2),(4,5))\) | two points | measure between 2 points |
polygon | polygon\(((0,0),(3,4),(4,2),(2,-1))\) | n points | closed plane figure made of points |
Polar Coordinates
Variable | Try typing... | Description |
---|---|---|
\(\theta\) | theta | the direction or the angle of rotation from the positive x-axis |
\(r\) | r | the distance from the origin to the point |
Constants and Variables
Constant or Variable | Try typing... | Description |
---|---|---|
\(\pi\) | pi | ratio of a circle’s circumference to its diameter |
\(\tau\) | tau | ratio of a circle’s circumference to its radius (or \(2\pi\)) |
\(e\) | e | base of the natural logarithm |
~ | ~ | indicates the regression model to be used to model the relationship between two sets of data \((x_{1},x_2)\) |
\(\infty\) | infinity | an unbounded quantity |
width | width | the width of the viewport (in pixels) |
height | height | the height of the viewport (in pixels) |
Four Function Calculator
Function | Try typing... | Description |
---|---|---|
square root | sqrt | finds the square root of a number |
answer | ans | uses the answer from the previous expression line |
Scientific Calculator
Function | Try typing... | Description |
---|---|---|
absolute value | \(|-5|\) | absolute value of a number (distance between that number and 0) |
\(\pi\) | pi | ratio of a circle’s circumference to its diameter |
nth root | nthroot | nth root of a number |
percent | % | percent of a number |
fraction | / or frac | type a fraction |
sine | sin(\(\pi\)) | sine of an angle |
cosine | cos(\(\pi\)) | cosine of an angle |
tangent | tan(\(\pi\)) | tangent of an angle |
arcsine | sin\(^{-1}\)(\(\pi\)) | inverse of the sine of an angle |
arccosine | cos\(^{-1}\)(\(\pi\)) | inverse of the cosine of an angle |
arctangent | tan\(^{-1}\)(\(\pi\)) | inverse of the tangent of an angle |
mean | mean\((1,5,5,10)\) | average of a list of numbers |
standard deviation | stdev\((1,5,5,10)\) | sample standard deviation of a list of numbers |
standard deviation population | stdevp\((1,5,5,10)\) | population standard deviation of a list of numbers |
permutation | nPr\((6,2)\) | the number of ways to arrange \(r\) distinct objects from a set of \(n\) distinct objects (the order of the objects matters) |
combination | nCr\((6,2)\) | the number of ways to choose \(r\) objects from a set of \(n\) distinct objects (the order of the objects does not matter) |
factorial | \(4!\) | product of all positive integers less than or equal to the given number |
natural logarithm | ln\((e)\) | natural log of the given number |
logarithm | log\((100)\) | logarithm of of the given number |
e | \(e\) | base of the natural logarithm |
round | round\((1.3254, 2)\) | round the given value to the nearest integer or given place value |
Function | Try typing... | Description |
---|---|---|
matrix template | matrix | shortcut to create a 2x2 matrix |
reduced row echelon format | rref\((A)\) | reduces matrix to row echelon form |
determinant | det\((A)\) | determinant of a square matrix |
trace | trace\((A)\) | sum of the diagonal of a matrix |
inverse | \(A^{-1}\) | inverse matrix |
square | \(A^{2}\) | square the matrix |
transpose | \(A^{T}\) | transpose the matrix |
Below you will find the list of functions supported in the geometry tool. Any of the functions supported in the graphing calculator will also work in this tool.
Geometry Tools
Function | Example with Arguments | Arguments | Description |
---|---|---|---|
midpoint | segment or 2 points | point equidistant from 2 endpoints of a segment or between two points | |
intersection | 2 intersecting lines, circles, or arcs | common point between 2 objects | |
segment | 2 points | part of a line with 2 endpoints | |
line | 2 points | collection of points in a straight path | |
ray | 2 points | part of a line with only one endpoint | |
parallel | line object and a point | lines that do not intersect in the same plane | |
perpendicular | line object and a point | lines that intersect in a plane at a right angle | |
anglebisector | angle | creates a ray that splits an angle into two congruent angles | |
circle | center point and another point, segment, or number | collection of points equidistant from a center | |
arc | 3 points | curved path through 3 points on the same circle | |
angle | 3 points | amount of rotation from one line to the other about a common vertex | |
directed angle | 3 points | measured angle (positive counter-clockwise and negative clockwise) | |
polygon | n points | closed plane figure made of points and segments | |
glider | object then a number - usually between 0 and 1 from the start to the end | point restricted to another object that follows that object’s path | |
vector | start point and end point | marker that shows both a direction and a magnitude |
Properties & Measurements
Function | Example with Arguments | Arguments | Description |
---|---|---|---|
length | segment | measure of a segment | |
distance | 2 points | measure between 2 points | |
area | polygon | measure of space contained by a polygon | |
perimeter | polygon | total length of all segments of a polygon | |
vertices | polygon | intersection points of the segments of a polygon | |
angles | polygon | measured rotations for each pair of adjacent segments in a polygon | |
directed angles | polygon | angles measured with direction in a polygon | |
segments | polygon | edges of a polygon | |
radius | circle or arc | measured distance from center to circumference of a circle | |
center | circle or arc | location of the point equidistant to the edge of a circle or arc | |
coterminal | angle or directed angle | angles that share an initial & terminal side (ex: \(30°\) & \(-330°)\) | |
supplement | directed angle | two adjacent angles that form a straight angle | |
vector.start | vector | initial/base point of a vector marker | |
vector.end | vector | tail point of a vector marker |
Transformations
Function | Example with Arguments | Arguments | Description |
---|---|---|---|
dilation | object, then a point and a number | increases or decreases the size of an object by a specific scale factor from a given point | |
rotation | object, then a point and a number | turns an object about a point by a directed angle | |
reflection | object, then a line, segment, ray, or vector | mirrors each point in an object across a given line | |
translation | object, then 2 points or a vector | moves every point of an object by the same distance in a given direction |
Below you will find the list of functions supported in the 3D calculator. Most of the functions supported in the graphing calculator will also work in this tool.
Polar Coordinates
Variable | Try typing... | Description |
---|---|---|
\(\rho\) | rho | distance between the origin and the point in 3D spherical coordinates |
\(\theta\) | theta | direction or the angle of rotation from the positive x-axis |
\(\phi\) | phi | angle between the ray from the origin and the positive z-axis |
\(r\) | r | distance from the origin to the point |
Geometry
Function | Try typing... | Arguments | Description |
---|---|---|---|
segment | segment\(((0,0,0),(2,2,2))\) | two points | part of a line with two endpoints |
triangle | triangle\(((0,0,0),(2,2,2),(1,3,2))\) | three 3D points | polygon with three sides and vertices |
sphere | sphere\(((0,0,0),1)\) | center point and radius value | 3D surface where every point is equidistant from a center point |
vector | vector\(((0,0,0),(1,1,1))\) | start point and end point | marker that shows both a direction and a magnitude |
dot product | \(v_1 * v_2\) | 2 vectors | multiplies the x components, y components, and z components and sums the result |
cross product | \(v_1\) cross \(v_2\) | 2 vectors | graphs the vector perpendicular to the plane containing the original 2 vectors |
length | length\((v_1)\) | 1 vector or segment | measure of a vector |
distance | distance\(((0,0,0),(3,3,3))\) | two points | measure between two points |
midpoint | midpoint\(((0,0,0),(3,3,3))\) | segment or two points | point equidistant between two points |
vector.start | vector.start | vector | initial/base point of a vector marker |
vector.end | vector.end | vector | tail point of a vector marker |