SMO Senior · 5. Trigonometry
Read signs from the unit circle, rewrite powers and mixed terms with double angles, find extreme values of $a\sin t+b\cos t$, use the sine and cosine rules, and collapse products and long sums by doubling and pairing.
Use quadrants, reduction formulas and addition formulas without sign errors.
Evaluate symmetric expressions with $(\sin x\pm\cos x)^2$, double angles and power sums.
Find the range of $c+a\sin t+b\cos t$ and of quadratic expressions in $\sin$ and $\cos$.
Apply the sine and cosine rules in triangle problems.
Collapse products and sums with product-to-sum formulas, doubling and pairing, including a Round 2 proof.