| sin(3θ) | 3sinθ−4sin3θ | Cubic polynomial in sine - derived from angle addition formulas |
| cos(3θ) | 4cos3θ−3cosθ | Cubic polynomial in cosine - fundamental for Chebyshev polynomials |
| tan(3θ) | 1−3tan2θ3tanθ−tan3θ | Rational function - undefined when 3tan²θ = 1, i.e., tanθ = ±√3/3 |
| csc(3θ) | 3−4sin2θcscθ | Reciprocal form involving original cosecant - undefined when sin(3θ) = 0 |
| sec(3θ) | 4cos2θ−3secθ | Reciprocal form involving original secant - undefined when cos(3θ) = 0 |
| cot(3θ) | 3cot2θ−1cot3θ−3cotθ | Rational function in cotangent - undefined when tan(3θ) = 0 |