Equivalent Representations of Trigonometric Functions
Some trig equalities hold for every angle: the Pythagorean identity, the sum and difference formulas, and the double-angle family they generate. Others are inventions, sine distributed over a sum, a 2 pulled through the function, and a single numeric test kills each of them. This topic separates the two and then puts the real ones to work rewriting expressions and converting mixed equations into a single function of a single angle.
The failure modes are inventing linearity that trig does not have, and solving in ways that discard answers: dividing both sides by a trig factor that can be zero, or reporting one solution family when the period supplies more. The lesson drills the numeric-test habit and the factor-never-divide discipline side by side.
The work
3 ways in · any order
Lesson
Equivalent Representations of Trigonometric Functions
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Real identities, fake identities, and the difference one test angle makes. The lesson builds the Pythagorean, sum, and double-angle tools, then turns them on equations with the factor-never-divide rule that keeps all four solutions where dividers keep two. Ten scenarios close it out.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 3.12 misconceptions: distributing trig functions over sums and doubles, and losing solution families while solving. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.