cosd — Cosine of angles expressed in degrees with MATLAB-exact values at canonical multiples.
y = cosd(x) evaluates the cosine of each angle in x, interpreting the values in degrees rather than radians. The implementation reduces the angle modulo 360 and special-cases 0, 60, 90, 120, and 180 (and their negative/wrapped counterparts) so the result matches MATLAB's exact 0, ±0.5, and ±1 values without floating-point noise.
How cosd 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 90 and exactly ±1 at multiples of 180.
- Returns exactly ±0.5 at multiples of 60 and 120.
- Complex inputs delegate to the analytic extension of
cosafter 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
Cosine of a canonical degree angle
y = cosd(60)Expected output:
y = 0.5Cosine of multiples of 90 returns exactly zero
y = cosd([90 270])Expected output:
y = [0 0]Cosine of a vector of common angles
angles = [0 30 45 60 90];
y = cosd(angles)Expected output:
y = [1 0.8660 0.7071 0.5 0]FAQ
Why does cosd(90) return exactly zero?⌄
MATLAB guarantees an exact zero at multiples of 90 to avoid floating-point noise from pi. RunMat reduces the angle modulo 360 and short-circuits the canonical cases before delegating to cos.
Is cosd(x) equivalent to cos(x*pi/180)?⌄
Mathematically yes, but the floating-point result differs at canonical angles because pi/180 is not exact in binary floating point. cosd returns the exact MATLAB values at multiples of 60, 90, 120, and 180.
Does cosd 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 · cosh · deg2rad · rad2deg · sin · sind · sinh · tan · tand · 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 cosd works, line by line, in Rust.
- View cosd.rs on GitHub
- Learn how the runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
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