costhetak

Costhetak is a term encountered in some mathematical writings and programming contexts as a compact notation for the cosine of a k-th angle, written informally as costhetak. It is not a standard mathematical function or operator, but a convenience alias used when a sequence of angles is indexed by an integer k. In formal contexts the expression would typically appear as cos(θ_k) or cos θ_k, with θ_k denoting the angle associated with index k.

Usage and context

Costhetak appears most often in lecture notes, worksheets, or code comments where an indexed angle sequence is being manipulated. It can simplify expressions involving sums or series that run over k, such as a term-by-term cosine evaluation. In practice, its meaning should be defined within the text or code to avoid ambiguity, since different authors may adopt different conventions for θ_k.

Notation and interpretation

When costhetak is used, θ_k should be specified to prevent confusion. If the angle sequence is defined by θ_k = θ_0 + kΔ, then costhetak means cos(θ_0 + kΔ). The values of costhetak depend on the chosen θ_0 and Δ and can be computed accordingly for any integer k.

Example

Suppose θ_k = π/3 + k(π/6). Then costhetak for k = 0, 1, 2, 3 is cos(π/3) = 0.5, cos(π/2) = 0, cos(2π/3) = -0.5, and cos(5π/6) ≈ -0.866.

Notes

Because costhetak is not a widely standardized term, it is important to define it explicitly whenever it appears in a document or program. When clarity is required, writing cos(θ_k) is preferred.

See also

Cosine, Theta, Trigonometric functions, Index notation.