Exact unit-circle values and reconstruction

Exact unit-circle values and reconstruction

Build reliable precalculus trigonometry by connecting exact sine, cosine and tangent values to coordinates and special triangles. This practice set develops reconstruction alongside recall: learners interpret a unit-circle diagram, reduce negative and multi-turn angles, and use quadrant information to preserve signs.

Questions include reciprocal ratios at canonical angles, coordinate pairs, comparisons of radical values and a circular-position application. Error-analysis items challenge familiar mistakes such as treating trigonometric functions as linear operations or confusing a zero coordinate with an undefined quotient. Both single-select and multiselect tasks require checking the complete claim.

Before beginning, review radians, reference angles, special right triangles and the coordinate definitions of the six trigonometric functions. Work exactly on scratch paper and simplify radicals before looking at the choices. The authored practice progresses from geometric interpretation to transfer and justification; each item remains independent if the app shuffles it.

Detailed explanations show the relevant geometry, sign choice and answer check. Use missed objectives to choose targeted practice rather than treating a total score as proof of mastery. This set prepares learners for trigonometric identities and graphs; it does not require general angle-addition formulas.