6 Trig Functions Calculator

Trigonometry is an essential area of mathematics that deals with the relationships between angles and sides of triangles. At the heart of this field are the six fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. Each of these plays a crucial role in geometry, physics, engineering, and signal processing.

6 Trig Functions Calculator

What Are the Six Trigonometric Functions?

The six primary trigonometric functions are:

  1. Sine (sin)
  2. Cosine (cos)
  3. Tangent (tan)
  4. Cotangent (cot)
  5. Secant (sec)
  6. Cosecant (csc)

Each of these functions represents a unique ratio of sides in a right triangle or values on the unit circle.

Why Use the 6 Trig Functions Calculator?

✅ Quickly calculates all six trig functions
✅ Accepts input in degrees or radians
✅ Supports positive and negative angles
✅ Great for checking homework or solving real-world problems
✅ Instant results with zero manual effort

How to Use the 6 Trig Functions Calculator

Step-by-Step Instructions:

  1. Choose Angle Unit
    Select whether your input is in degrees or radians.
  2. Enter the Angle
    Input any real number (e.g., 30°, π/4, –45°, etc.).
  3. Click “Calculate”
    The calculator returns all six trig functions instantly.
  4. View Results
    Results are displayed clearly:
    • sin(θ)
    • cos(θ)
    • tan(θ)
    • cot(θ)
    • sec(θ)
    • csc(θ)

Trig Functions Definitions (Plain Text Formulas)

Given a right triangle or unit circle, here are the six trig functions:

  1. sin(θ) = opposite / hypotenuse
  2. cos(θ) = adjacent / hypotenuse
  3. tan(θ) = opposite / adjacent = sin(θ) / cos(θ)
  4. cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ)
  5. sec(θ) = 1 / cos(θ)
  6. csc(θ) = 1 / sin(θ)

For angles beyond 0°–90°, the unit circle is used to calculate values.

Example 1: Input Angle in Degrees

Angle = 30°

  • sin(30°) = 0.5
  • cos(30°) ≈ 0.866
  • tan(30°) ≈ 0.577
  • cot(30°) ≈ 1.732
  • sec(30°) ≈ 1.154
  • csc(30°) = 2

Example 2: Input Angle in Radians

Angle = π/4 radians (≈ 0.7854)

  • sin(π/4) ≈ 0.7071
  • cos(π/4) ≈ 0.7071
  • tan(π/4) ≈ 1
  • cot(π/4) ≈ 1
  • sec(π/4) ≈ 1.4142
  • csc(π/4) ≈ 1.4142

Domain & Range of Each Function

FunctionDomainRange
sin(θ)All real numbers[–1, 1]
cos(θ)All real numbers[–1, 1]
tan(θ)All real numbers except odd multiples of π/2(–∞, ∞)
cot(θ)All real numbers except multiples of π(–∞, ∞)
sec(θ)All real numbers except odd multiples of π/2(–∞, –1] ∪ [1, ∞)
csc(θ)All real numbers except multiples of π(–∞, –1] ∪ [1, ∞)

Applications of Trigonometric Functions

  • 📐 Geometry: Solving triangles, angle measurement
  • 📡 Physics: Wave behavior, oscillations, optics
  • ⚙️ Engineering: Rotational motion, signal processing
  • 🌍 Geography: GPS systems, navigation, mapping
  • 🎓 Education: Essential in algebra, calculus, and pre-calculus

Benefits of This Calculator

  • 🔹 Eliminates need for a scientific calculator
  • 🔹 Returns all six functions instantly
  • 🔹 Great for learning or checking math homework
  • 🔹 Handles any valid angle input
  • 🔹 Converts seamlessly between degrees and radians

20 Frequently Asked Questions (FAQs)

1. What is a trigonometric function?

It’s a function that relates angles to side ratios in right triangles.

2. What are the six trigonometric functions?

Sine, cosine, tangent, cotangent, secant, and cosecant.

3. What’s the difference between radians and degrees?

Degrees divide a circle into 360 parts; radians are based on π, with 2π radians = 360°.

4. Can I use this calculator for negative angles?

Yes, it handles both positive and negative angles.

5. What is sin(90°)?

1

6. What is cos(90°)?

0

7. What is tan(90°)?

Undefined (division by zero)

8. What is cot(0°)?

Undefined

9. What’s the use of sec and csc?

They’re the reciprocals of cosine and sine, useful in advanced calculations.

10. What angle gives tan(θ) = 1?

θ = 45° or π/4 radians

11. Is this calculator accurate?

Yes, results are accurate up to 4+ decimal points.

12. What if I enter a decimal like 22.5°?

The calculator will still compute all six values precisely.

13. What is the input range for the calculator?

Any real number in degrees or radians.

14. Does it show undefined values?

Yes, it will inform you when a function is undefined (like tan(90°)).

15. Can I use it for circular functions?

Yes, all inputs are interpreted on the unit circle.

16. Is it good for high school students?

Absolutely. It’s ideal for students learning trigonometry.

17. Can I copy the results?

Yes, you can easily copy and paste results for assignments or reports.

18. Is it available on mobile?

Yes, fully responsive on mobile and tablets.

19. Is there a graph feature?

Not in this tool, but you can pair it with graphing tools.

20. Is it free to use?

Yes, 100% free and unlimited usage.

Final Thoughts

The 6 Trig Functions Calculator is a one-stop solution for finding sine, cosine, tangent, cotangent, secant, and cosecant values. Whether you're working in degrees or radians, this tool helps you learn faster, check your work, and solve problems accurately.