9.6 Periodic and triangle models

Ideas in this lesson

Build a periodic model

Use maximum and minimum to find midline and amplitude; use a known maximum or minimum to set the phase.

Interpret a sinusoidal model

Distinguish angular frequency from cycles per unit time. Period is the time required for one complete cycle.

Law of cosines

Relate two sides and their included angle to the opposite side. Keep squared units until the final square root.

Law of sines

Pair each side with its opposite angle. Distinguish an acute-angle condition from an ambiguous side-side-angle case.

The ambiguous sine-rule case

Check both sine-compatible angles and reject triangles whose angle sum is not below a straight angle.