Evaluating Trig Functions at Special Angles

Pre-Calculus · Axiom Academy

EXAMPLE Evaluating Trig Functions at Special Angles Reading sine and cosine straight off the unit circle Evaluate each of these special-angle values exactly. On the unit circle, a point at angle has coordinates , so the x -coordinate gives cosine and the y -coordinate gives sine. Each marked point sits at (cos θ, sin θ) . Read sine from the height (y) and cosine from the horizontal position (x). Nice work — you evaluated all five special-angle values straight from the unit circle. Coordinates are the values: a point at angle is — sine is the height, cosine is the horizontal position. Reference angle + quadrant sign: outside Quadrant I, find the acute reference angle, then attach the sign for that quadrant ( is + in Q2, is - in Q3). Quadrantal angles are exact: at 270° the point is (0,-1) , so . Memorize the first-quadrant values and the unit circle hands you every special angle.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.