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
| x | Plug in x | ƒ(x) = sin(x) | Ordered Pair |
|---|---|---|---|
| 2π | sin([2π]) | -2.4492935982947E-16 | (2π, -2.4492935982947E-16) |
| 11π/6 | sin([11π/6]) | -0.5 | (11π/6, -0.5) |
| 7i/4 | sin([7i/4]) | -0.70710678118655 | (7i/4, -0.70710678118655) |
| 5π/3 | sin([5π/3]) | -0.86602540378444 | (5π/3, -0.86602540378444) |
| 3π/2 | sin([3π/2]) | -1 | (3π/2, -1) |
| 4π/3 | sin([4π/3]) | -0.86602540378444 | (4π/3, -0.86602540378444) |
| 5π/4 | sin([5π/4]) | -0.70710678118655 | (5π/4, -0.70710678118655) |
| 7π/6 | sin([7π/6]) | -0.5 | (7π/6, -0.5) |
| π | sin([π]) | 1.2246467991474E-16 | (π, 1.2246467991474E-16) |
| 5π/6 | sin([5π/6]) | 0.5 | (5π/6, 0.5) |
| 3π/4 | sin([3π/4]) | 0.70710678118655 | (3π/4, 0.70710678118655) |
| 2π/3 | sin([2π/3]) | 0.86602540378444 | (2π/3, 0.86602540378444) |
| π/2 | sin([π/2]) | 1 | (π/2, 1) |
| π/3 | sin([π/3]) | 0.86602540378444 | (π/3, 0.86602540378444) |
| π/4 | sin([π/4]) | 0.70710678118655 | (π/4, 0.70710678118655) |
| π/6 | sin([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 0.5Determine the x-intercept
The x-intercept is found when y is set to 0The 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 enterThe 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 existThe 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)
(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)
Keep Practicing
Common Core State Standards In This Lesson
CCSS.MATH.CONTENT.6.EE.C.9,CCSS.MATH.CONTENT.8.F.A.1
What is the Answer?
(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)
(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. Table of Functions Calculator
This calculator has 1 input.
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
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
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