## Enter function:

With the function that you entered of sin(x), plot points, determine the intercepts, domain, range

Since you did not specify a qualifying variable or function notation in your expression, we will assume y
y = sin(x)

## Determine function type:

Since we have one of the standard trigonometric functions:
this is a trigonometric function

## Now Plot points from pi/6 to 2pi

xPlug in xƒ(x) = sin(x)Ordered Pair
sin([])-2.4492935982947E-16(2π, -2.4492935982947E-16)
11π/6sin([11π/6])-0.5(11π/6, -0.5)
7i/4sin([7i/4])-0.70710678118655(7i/4, -0.70710678118655)
5π/3sin([5π/3])-0.86602540378444(5π/3, -0.86602540378444)
3π/2sin([3π/2])-1(3π/2, -1)
4π/3sin([4π/3])-0.86602540378444(4π/3, -0.86602540378444)
5π/4sin([5π/4])-0.70710678118655(5π/4, -0.70710678118655)
7π/6sin([7π/6])-0.5(7π/6, -0.5)
πsin([π])1.2246467991474E-16(π, 1.2246467991474E-16)
5π/6sin([5π/6])0.5(5π/6, 0.5)
3π/4sin([3π/4])0.70710678118655(3π/4, 0.70710678118655)
2π/3sin([2π/3])0.86602540378444(2π/3, 0.86602540378444)
π/2sin([π/2])1(π/2, 1)
π/3sin([π/3])0.86602540378444(π/3, 0.86602540378444)
π/4sin([π/4])0.70710678118655(π/4, 0.70710678118655)
π/6sin([π/6])0.5(π/6, 0.5)

## Determine the y-intercept:

The y-intercept is found when x is set to 0. From the grid above, our y-intercept is 0.5

## Determine the x-intercept

The x-intercept is found when y is set to 0
The y-intercept is found when y is set to 0. From the grid above, our x-intercept is 0

## Determine the domain of the function:

The domain represents all values of x that you can enter
The domain is (-∞, ∞) or All Real Number

## Determine the range of the function:

The range is all the possible values of y or ƒ(x) that can exist
The range is [-1, 1]

(2π, -2.4492935982947E-16)
(11π/6, -0.5)
(7i/4, -0.70710678118655)
(5π/3, -0.86602540378444)
(3π/2, -1)
(4π/3, -0.86602540378444)
(5π/4, -0.70710678118655)
(7π/6, -0.5)
(π, 1.2246467991474E-16)
(5π/6, 0.5)
(3π/4, 0.70710678118655)
(2π/3, 0.86602540378444)
(π/2, 1)
(π/3, 0.86602540378444)
(π/4, 0.70710678118655)
(π/6, 0.5)

#### You have 2 free calculationss remaining

(2π, -2.4492935982947E-16)
(11π/6, -0.5)
(7i/4, -0.70710678118655)
(5π/3, -0.86602540378444)
(3π/2, -1)
(4π/3, -0.86602540378444)
(5π/4, -0.70710678118655)
(7π/6, -0.5)
(π, 1.2246467991474E-16)
(5π/6, 0.5)
(3π/4, 0.70710678118655)
(2π/3, 0.86602540378444)
(π/2, 1)
(π/3, 0.86602540378444)
(π/4, 0.70710678118655)
(π/6, 0.5)
##### How does the Function Calculator work?
Free Function Calculator - Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.
This calculator has 1 input.

### What 5 formulas are used for the Function Calculator?

The y-intercept is found when x is set to 0
The x-intercept is found when y is set to 0
The domain represents all values of x that you can enter
The range is all the possible values of y or ƒ(x) that can exist

For more math formulas, check out our Formula Dossier

### What 4 concepts are covered in the Function Calculator?

domain
Set of all possible input values which makes the output value of a function valid
function
relation between a set of inputs and permissible outputs
ƒ(x)
ordered pair
A pair of numbers signifying the location of a point
(x, y)
range
Difference between the largest and smallest values in a number set