Trigonometric Function Calculator
Enter an angle to calculate sine, cosine, and other trigonometric functions.
What Is a Trigonometric Function Calculator?
A trigonometric function calculator instantly computes sine (sin), cosine (cos), tangent (tan), and other trigonometric values from any angle you enter. Whether you’re a student tackling homework, an engineer calculating structural loads, or a developer working on graphics programming, this tool eliminates tedious manual calculations and delivers accurate results in seconds.
Key Features
This calculator packs everything you need for trigonometric computations into one intuitive interface.
Switch seamlessly between degrees and radians with a single click. High school math typically uses degrees, while college-level calculus and physics rely on radians—this tool handles both without hassle.
The interactive unit circle visualization shows exactly where your angle falls on the circle. Watch the point move as you change values, making it easy to grasp how sin corresponds to the y-coordinate and cos to the x-coordinate.
Quick-access preset buttons for common angles (0°, 30°, 45°, 60°, 90°, 180°) let you instantly recall standard trigonometric values without typing anything.
How to Use This Calculator
Getting your results takes just three simple steps.
First, select your preferred unit—degrees or radians. Then enter your angle value in the input field. Finally, click “Calculate” to see your results instantly displayed alongside the unit circle visualization.
Need more detail? Click “Show Reciprocal Functions” to reveal cosecant (csc), secant (sec), and cotangent (cot) values. You can also save your results as an image for reports or study notes.
Understanding Trigonometric Functions
Trigonometric functions describe relationships between angles and sides in right triangles—and extend far beyond basic geometry.
Sine (sin) represents the ratio of the opposite side to the hypotenuse. On the unit circle, it equals the y-coordinate of the point at that angle.
Cosine (cos) is the ratio of the adjacent side to the hypotenuse, corresponding to the x-coordinate on the unit circle.
Tangent (tan) equals sine divided by cosine, or the ratio of opposite to adjacent sides.
The reciprocal functions—cosecant (1/sin), secant (1/cos), and cotangent (1/tan)—appear frequently in advanced mathematics and physics applications.
Real-World Applications
Trigonometry powers countless technologies and professions you encounter every day.
Architects and engineers use trigonometric functions to calculate building heights, bridge spans, and roof pitches. Surveyors rely on these calculations to map terrain and determine property boundaries with precision.
In physics, trig functions describe oscillations, wave behavior, and circular motion. From pendulum swings to electromagnetic waves, these mathematical tools are essential for understanding how the physical world works.
Game developers and 3D animators use trigonometry constantly. Every rotation, camera angle, and character movement in video games involves sin and cos calculations running behind the scenes.
Frequently Asked Questions
How do I convert between degrees and radians?
Multiply degrees by π/180 to get radians. For example, 180° equals π radians, and 90° equals π/2 radians. This calculator automatically displays the converted value, so you can see both units at once.
Why can’t I calculate tan(90°)?
Tangent equals sin divided by cos. At 90°, cos equals zero, making the division undefined. The calculator displays “undefined” or “infinity” for these special cases.
Can I save my calculation results?
Yes. Click “Save as Image” to download a snapshot that includes the unit circle diagram and all calculated values—perfect for homework submissions or study materials.
Does this calculator accept negative angles?
Absolutely. Negative angles (like -45°) measure clockwise rotation from the positive x-axis. The calculator handles these correctly and displays them accurately on the unit circle.