What is the Trigonometry Calculator?
The Trigonometry Calculator is a comprehensive tool for computing trigonometric functions and their inverses. Whether you need to find the sine of an angle or determine what angle produces a specific cosine value, this calculator provides instant, accurate results.
Supported Functions
This calculator supports all six primary trigonometric operations:
sin
cos
tan
arcsin
arccos
arctan
Key Features
Dual Mode Support
Switch between degrees and radians instantly for maximum flexibility in your calculations.
Exact Values
Displays mathematical expressions like √2/2 for special angles alongside decimal approximations.
Related Values
Shows reciprocal functions (csc, sec, cot) alongside results for comprehensive understanding.
Real-time Calculation
Results update instantly as you type—no calculate button needed.
- 1. What is the Trigonometry Calculator?
- 2. How to Use the Calculator
- 3. Features
- 4. Frequently Asked Questions
- 4.1. What is the difference between degrees and radians?
- 4.2. Why does tan(90°) show infinity?
- 4.3. What are inverse trigonometric functions?
- 4.4. Why can I only enter values between -1 and 1 for arcsin and arccos?
- 4.5. What are the exact values shown for special angles?
- 4.6. What are csc, sec, and cot?
- 4.7. How accurate are the calculations?
- 4.8. Can I use this calculator offline?
How to Use the Calculator
Select a Function
Click on one of the six tabs at the top to choose your trigonometric function:
- sin, cos, tan - Enter an angle to get the trigonometric value
- arcsin, arccos, arctan - Enter a value to get the corresponding angle
Choose Your Angle Mode
Click DEG or RAD to switch between degrees and radians:
Degrees Mode
- Enter angles in degrees
- Examples: 45, 90, 180
- Full circle = 360°
Radians Mode
- Enter angles in radians
- Examples: π/4, π/2, π
- Full circle = 2π
Enter Your Value
Type your number in the input field. The result updates automatically as you type.
3.14159/4 for π/4.Read Your Results
The calculator displays comprehensive information:
- Primary Result - The main calculated value
- Exact Value - Mathematical expression for special angles (when applicable)
- Related Values - Reciprocal function and angle in the other unit
Features
Six Trigonometric Functions
Calculate all primary trig functions and their inverses in one place. Switch between functions with a single click using the tab navigation.
Degrees and Radians Support
Toggle between degree mode (DEG) and radian mode (RAD) instantly. The calculator automatically converts your input and displays results in your chosen unit.
Exact Values for Special Angles
For special angles like 30°, 45°, and 60°, the calculator shows exact mathematical expressions:
| Function | Angle | Exact Value | Decimal |
|---|---|---|---|
| sin(30°) | 30° | 1/2 |
0.5 |
| sin(45°) | 45° | √2/2 |
≈ 0.7071 |
| cos(60°) | 60° | 1/2 |
0.5 |
| tan(45°) | 45° | 1 |
1.0 |
Reciprocal Functions
Along with your result, see the corresponding reciprocal function value:
csc (cosecant)
sec (secant)
cot (cotangent)
Real-time Calculation
Results update instantly as you type. No need to press a calculate button—just enter your value and see the result immediately.
Input Validation
The calculator validates your input and shows helpful error messages:
- Arcsin and arccos require values between -1 and 1
- Invalid expressions show clear error messages
- Undefined values (like tan(90°)) display infinity symbol
Special Angles Reference Table
Access a collapsible reference table showing trigonometric values for common angles from 0° to 180°. Perfect for quick lookups and verification.
Formula Reference
Each function tab displays the relevant formula, helping you understand the mathematical relationship being calculated.
Frequently Asked Questions
What is the difference between degrees and radians?
Degrees and radians are two ways to measure angles. A full circle is 360° or 2π radians.
Conversion formulas:
- Degrees to radians: multiply by
π/180 - Radians to degrees: multiply by
180/π
The calculator handles this conversion automatically when you switch modes.
Why does tan(90°) show infinity?
The tangent function equals sin/cos. At 90°, cos(90°) = 0, and dividing by zero is undefined.
Mathematically, tan approaches infinity as the angle approaches 90°. The same applies to 270° and other angles where cosine equals zero.
What are inverse trigonometric functions?
Inverse functions (arcsin, arccos, arctan) work backwards from regular trig functions. Instead of giving you a ratio from an angle, they give you an angle from a ratio.
Example: If sin(30°) = 0.5, then arcsin(0.5) = 30°
Regular Functions
- Input: Angle
- Output: Ratio
- Example: sin(30°) = 0.5
Inverse Functions
- Input: Ratio
- Output: Angle
- Example: arcsin(0.5) = 30°
Why can I only enter values between -1 and 1 for arcsin and arccos?
Since sine and cosine functions only output values between -1 and 1, their inverse functions can only accept inputs in that range.
Mathematical principle: There is no angle whose sine or cosine is greater than 1 or less than -1.
What are the exact values shown for special angles?
Special angles (0°, 30°, 45°, 60°, 90°, etc.) have trigonometric values that can be expressed as simple fractions or square roots.
Example: sin(45°) = √2/2 ≈ 0.7071
The calculator shows both the exact form and decimal approximation for better understanding and precision.
What are csc, sec, and cot?
These are reciprocal trigonometric functions:
- csc (cosecant) = 1/sin
- sec (secant) = 1/cos
- cot (cotangent) = 1/tan
The calculator shows these as related values when you calculate sin, cos, or tan.
How accurate are the calculations?
The calculator uses JavaScript's built-in Math functions with double-precision floating-point arithmetic.
Precision
Display
Can I use this calculator offline?
Yes! All calculations are performed locally in your browser using JavaScript.
Once the page is loaded, you can use the calculator without an internet connection. No data is sent to any server.
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