tand — Tangent of angles expressed in degrees with MATLAB-exact poles at +/-90 and exact zeros at multiples of 180.
y = tand(x) evaluates the tangent of each angle in x, interpreting the values in degrees rather than radians. The implementation reduces the angle modulo 360 and special-cases 0, 45, 90, 135, and 180 (and their negative/wrapped counterparts) so multiples of 180 return an exact 0, multiples of 45 return ±1, and the poles at +90 and -90 return +Inf and -Inf respectively.
How tand works
- Operates element-wise on scalars, vectors, matrices, and N-D tensors.
- Integer and logical inputs are promoted to double precision before evaluation.
- Returns exactly 0 at multiples of 180 and exactly ±1 at multiples of 45.
- Returns +Inf at +90 (and angles equivalent under modulo 360) and -Inf at -90 (and equivalent angles).
- Complex inputs delegate to the analytic extension of
tanafter scaling bypi/180; exact-value treatment for complex operands is deferred. - Output shape matches the input shape; non-finite inputs propagate as
NaN. - String inputs are unsupported and raise a builtin-scoped error.
Examples
Tangent of a canonical degree angle
y = tand(45)Expected output:
y = 1Tangent at the +/-90 poles returns +/-Inf
y = tand([90 -90])Expected output:
y = [Inf -Inf]Tangent of a multiple of 180 returns exactly zero
y = tand(180)Expected output:
y = 0FAQ
Why does tand(90) return Inf instead of a very large finite number?⌄
MATLAB defines tand(90) = Inf and tand(-90) = -Inf at the poles. Naively evaluating tan(90*pi/180) would return a huge finite number because pi/180 is not exact in floating point, so RunMat short-circuits the poles to match MATLAB.
Is tand(x) equivalent to tan(x*pi/180)?⌄
Mathematically yes, but the floating-point result differs at canonical angles. tand guarantees exact values at multiples of 45 and 180, and infinite values at +/-90.
Does tand support arrays?⌄
Yes. Scalars, vectors, matrices, and N-D tensors are all handled element-wise; the shape of the input is preserved.
Related Math functions
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · deg2rad · rad2deg · sin · sind · sinh · tan · tanh
Elementwise
abs · angle · complex · conj · double · exp · expm1 · factorial · gamma · hypot · imag · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · sign · single · sqrt · times
Reduction
all · any · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · mean · median · min · nnz · prod · std · sum · trapz · var
Structure
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how tand works, line by line, in Rust.
- View tand.rs on GitHub
- Learn how the runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code — faster, on any GPU, with no license required.
- Simulations that took hours now take minutes. RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed.
- Start running code in seconds. Open the browser sandbox or download a single binary. No license server, no IT ticket, no setup.
- A full development environment. GPU-accelerated 2D and 3D plotting, automatic versioning on every save, and a browser IDE you can share with a link.