1. Enter Value and Select Function Type:
2. Calculated Values:
Unit Circle Visualisation
How to Use the Functions Calculator ƒ(x)
This calculator evaluates various mathematical functions for a given input value x. It supports basic trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions.
1. Enter Input Value (x):
- In the “Enter Value (x)” field, type the number for which you want to calculate the functions.
2. Select Unit for x (if applicable):
- If you are calculating Basic Trigonometric or Hyperbolic functions and your input
xrepresents an angle, choose whether it’s in “Degrees” or “Radians” from the “Unit for x” dropdown. - For Inverse Trigonometric and Inverse Hyperbolic functions, the input
xis typically a ratio or value, not an angle, so this unit selection primarily affects the *output unit* for inverse trigonometric results (which are angles).
3. Choose Function Group:
- From the “Function Group” dropdown, select the category of functions you are interested in.
4. Calculate:
- Click the “Calculate ƒ(x)” button.
5. Interpret the Results:
- A table will appear showing the selected functions and their calculated values for your input
x. - If a function is undefined for the given
x, the table will indicate “Undefined” or “Invalid Input”. - Unit Circle Visualisation: If you selected “Basic Trigonometric” functions and provided an angle, a dynamic unit circle diagram will appear.
6. Clearing Inputs:
- Click “Clear All” to reset all input fields and results.
Evaluating ƒ(x): Your Guide to Trigonometric, Inverse, and Hyperbolic Functions
The Essence of ƒ(x): Understanding Mathematical Functions
In mathematics, a function, ƒ(x), is a rule that takes an input (x) and produces a specific output. This calculator explores trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions, each with unique traits and uses in science, engineering, and math.
Basic Trigonometric Functions: The Language of Cycles
Sine (sin), Cosine (cos), Tangent (tan), and their reciprocals (csc, sec, cot) describe cyclical phenomena. They’re defined using the unit circle: sin(x) is the y-coordinate, cos(x) is the x-coordinate of a point on the circle at angle x. Tan(x) = sin(x)/cos(x). Our calculator visualizes this.
Degrees vs. Radians
Angles are in degrees (360° circle) or radians (2π circle). Radians are standard in advanced math. This tool handles both for angle inputs.
Inverse Trigonometric Functions: Finding the Angle
These find the angle given a ratio (e.g., asin(y)=x if sin(x)=y). They return principal values, e.g., asin(x) is in [-90°, 90°]. Domains are restricted (e.g., asin(x) needs x in [-1,1]).
Hyperbolic Functions: Trigonometry of Hyperbolas
Defined with ex (e.g., sinh(x) = (ex-e-x)/2, cosh(x) = (ex+e-x)/2). Used in physics for shapes like hanging chains (catenary).
Inverse Hyperbolic Functions: Reversing Hyperbolic
These “undo” hyperbolic functions, often using natural logs (e.g., asinh(x) = ln(x+√(x²+1))). Domains apply (e.g., acosh(x) needs x ≥ 1).
“Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.” – Archimedes.
Using This Calculator
1. Input x. 2. Select unit if x is an angle. 3. Choose function group. 4. Click “Calculate”. 5. View results table and unit circle (for basic trig).
Conclusion: A Versatile Tool
This calculator offers a user-friendly way to evaluate a wide range of important mathematical functions, aiding learning and application.