Question 1

What is the difference between radians and degrees?

Accepted Answer

360° = 2π radians, so 1 rad ≈ 57.3°. To convert: radians = degrees × π/180. In math, sin and cos take radians by default; in everyday trigonometry degrees are often handier. The calculator supports both modes.

Question 2

When are sin and cos used?

Accepted Answer

Sine and cosine are the coordinates of a point on the unit circle. They model force projections and waves in physics, the law of sines in geometry, alternating current in engineering (I = I₀ sin(ωt)), and distances in navigation.

Question 3

What are hyperbolic functions?

Accepted Answer

sinh, cosh, and tanh are analogs of the trig functions defined on a hyperbola instead of a circle, e.g. cosh(x) = (eˣ + e⁻ˣ)/2. They describe the catenary (the shape of a hanging cable), special relativity, and certain probability distributions.

Question 4

How does the mod function work?

Accepted Answer

It returns the remainder of a division: 17 mod 5 = 2 (since 17 = 3×5 + 2). In code it is the % operator. Uses include checking parity (n mod 2), cyclic counters, hashing, and encryption. Note JavaScript gives (-7) % 3 = -1, unlike the mathematical convention.

Question 5

What are inverse trigonometric functions?

Accepted Answer

arcsin, arccos, and arctan return the angle for a given function value, e.g. arcsin(0.5) = 30° = π/6. Their ranges are restricted: arcsin to [−90°, 90°], arccos to [0°, 180°], arctan to (−90°, 90°). They are used to find angles in triangles and the direction of vectors.

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