tand — Compute element-wise tangent values for degree-based angles with MATLAB-compatible canonical handling.
y = tand(x) computes tangent using degree-based angles rather than radians. It follows MATLAB-compatible canonical handling for key multiples, including exact zeros at 180-degree multiples and poles at odd 90-degree multiples.
Syntax
Y = tand(X)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
X | Any | Yes | — | Input scalar, array, logical array, complex value, or gpuArray. |
Returns
| Name | Type | Description |
|---|---|---|
Y | Any | Element-wise tangent result with degree input semantics. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:tand:InvalidInput | Input cannot be interpreted as supported numeric/logical/complex data. | tand: invalid input |
RunMat:tand:Internal | Internal gather/conversion/allocation flow failed. | tand: internal error |
How tand works
- Operates element-wise on scalars, vectors, matrices, and N-D tensors.
- Documented single inputs return single and documented double inputs return double.
- Typed integers and logical inputs are independently gated RunMat extensions. Integer angles are reduced exactly modulo 360 before floating evaluation, so wide int64 and uint64 inputs are never rounded through a double angle mirror.
- 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. MATLAB's documented direct table and timetable calculation form is not implemented yet.
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 = 0Using tand with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how tand changes the result.
Run a small tand example, explain the result, then change one input and compare the output.
FAQ
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 · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tanh
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · typecast · uint16 · uint32 · uint8
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · secondordercone
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how tand is executed, line by line, in Rust.
- View the source for tand in Rust on GitHub
- Learn how the RunMat 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 blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
- Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.