Sine and Cosine Function Values
Every exact value on the exam is generated by three first-quadrant points: (√3/2, 1/2) at π/6, (√2/2, √2/2) at π/4, and (1/2, √3/2) at π/3. Any other special angle folds onto one of these by its reference angle, the acute angle to the x-axis, and then the quadrant decides the signs: cosine follows x (positive on the right half), sine follows y (positive on the top half). The axis angles 0, π/2, π, 3π/2 are read straight off the points (1,0), (0,1), (−1,0), (0,−1).
The mistakes are swaps and signs: trading which of 1/2 and √3/2 belongs to sine at a given angle, keeping first-quadrant signs after folding into another quadrant, and putting π at the top of the circle when the top belongs to π/2. The lesson drills the folding move and the two separate sign decisions until they are automatic.
The work
3 ways in · any order
Lesson
Sine and Cosine Function Values
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Three memorized points, one folding move, two sign decisions: that is the entire exact-value table. The lesson builds the 1/2, √2/2, √3/2 ladder with a built-in size check, then closes with ten scenarios of values across all four quadrants and the axis angles.
Diagnostic
10-item topic check
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Ten items spanning the Topic 3.3 misconception: coordinate swaps and quadrant sign errors at the special angles. 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.