Construct complete periodic graphs, compare finite rates and fit competing sinusoidal periods using new evidence. School algebra, unit-circle coordinates and graph reading suffice; calculus is not required.
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Horizontal repetition and vertical variation describe different features.
The period is the smallest positive input shift that repeats a nonconstant sinusoid. Its amplitude is half the difference between its maximum and minimum outputs. Their units follow the input and output respectively.
A graph must retain exclusions and separate branches.
Check its original denominator: tangent and secant require nonzero cosine; cotangent and cosecant require nonzero sine. A plotting line must never join branches across an excluded input.
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Periodic graph evidence: mixed practice
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Construct a complete sinusoid and separate output level, motion direction and concavity.
6 practice tasks.
Execute conditional periodic regression and expose ambiguity with unused inputs.
6 practice tasks.
Track transformed asymptotes and solve inequalities across all admissible intervals.
6 practice tasks.
Use reciprocal geometry to recover disconnected ranges, branch vertices and direction.
6 practice tasks.
