Trigonometric Functions Calculator
Calculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle.
This free online trigonometric functions calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Results
sin(θ)
0.707107
cos(θ)
0.707107
tan(θ)
1
csc(θ)
1.414214
sec(θ)
1.414214
cot(θ)
1
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Trigonometric Functions Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Trigonometric Functions Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Trigonometric Functions Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
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Arccos Calculator (Inverse Cosine)
Calculate the inverse cosine (arccos) of a value. Returns the angle whose cosine equals the input.
Arcsin Calculator (Inverse Sine)
Calculate the inverse sine (arcsin) of a value. Returns the angle whose sine equals the input.
Arctan Calculator (Inverse Tangent)
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About Trigonometric Functions Calculator
The six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — form the foundation of trigonometry. They relate angles to ratios of sides in right triangles and extend to all real numbers via the unit circle. Sine and cosine are the primary functions; the other four are derived from them. These functions are periodic, meaning they repeat their values at regular intervals: sin and cos have period 360° (2π), while tan and cot have period 180° (π). Trigonometric functions are essential in physics (wave motion, oscillation, rotation), engineering (signal processing, AC circuits), computer science (graphics, animation), and music (sound waves). This calculator evaluates all six functions simultaneously for any angle.
The Math Behind It
Formula Reference
Primary Functions
sin θ, cos θ, tan θ = sin θ / cos θ
Variables: θ = angle
Reciprocal Functions
csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
Variables: θ = angle
Worked Examples
Example 1: All six functions at 60°
Compute all six trig functions at θ = 60°.
All six values computed from the 30-60-90 triangle ratios.
Common Mistakes & Tips
- !Confusing degrees and radians — always check your calculator mode.
- !Forgetting that tangent and secant are undefined at 90°, 270°, etc.
- !Mixing up reciprocal pairs: csc goes with sin, sec goes with cos, cot goes with tan.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
What is the difference between sin and csc?
csc(θ) = 1/sin(θ). They are reciprocals of each other.
Which trig functions can have values greater than 1?
tan, cot, csc, and sec can all have absolute values greater than 1. Only sin and cos are bounded between −1 and 1.
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