Prove and apply key trigonometric identities, solve real-world triangle problems using sine/cosine laws, and master function transformations to model periodic behavior.
Prove and manipulate trigonometric identities fluently.
Solve any triangle using sine/cosine laws with area formulas.
Transform trig functions and analyze amplitude, period, and phase shifts.
Model periodic phenomena in physics, engineering, and climate data.
Lesson 4-1
Pythagorean, quotient, reciprocal, sum/difference, and double-angle identities with proofs and applications.
Lesson 4-2
Use sine and cosine laws for ambiguous cases, area formulas, navigation, and surveying problems.
Lesson 4-3
Amplitude, period, phase shift, and vertical shift; compose transformations to model periodic phenomena.
Identity manipulation develops proof techniques essential for advanced mathematics.
Triangle solving supports navigation, surveying, and physics problem solving.
Transformations of trig functions model periodic signals in engineering.