Unit 7 · Core unit
Rewriting trigonometric expressions into a form that can be evaluated or solved, and reporting every solution the interval demands.
What a strong answer looks like
A strong answer reports all solutions in the stated interval, not only the one a calculator returns.
Know
Reciprocal, quotient, and Pythagorean identities convert between the six functions and are the vocabulary of the unit.
Apply
Rewrite everything in sine and cosine when an expression resists simplification.
Watch out
Treating an identity as an equation to be solved rather than a transformation to apply.
Study move
Verify one identity by transforming a single side only.
Know
These produce exact values for angles that are sums or doubles of familiar ones.
Apply
Decompose an unfamiliar angle into familiar parts, then apply the identity.
Watch out
Assuming a trigonometric function distributes across a sum, which it does not.
Study move
Find an exact value for an angle expressed as a sum of two special angles.
Know
Because the functions repeat, the stated interval determines which solutions to report.
Apply
Solve for the trigonometric expression first, then find every angle in the interval producing it.
Watch out
Reporting only the calculator principal value and missing its reflection.
Study move
Solve a quadratic in sine and list every solution in one full turn.
Modeling drill
Solve a trigonometric equation with two solutions in one turn, showing how the second is found from symmetry.
