1.5.2—Exact trig values

The standard exact values sin, cos and tan at 0, π/6, π/4, π/3 and π/2 follow from 30–60–90 and 45–45–90 triangles, with signs set by the quadrant.

Reduce angles using periodicity and reference angles before applying the table. Keep radicals exact until a decimal is explicitly requested.

sin(5π/6)=sin(π−π/6)=1/2, while cos(5π/6)=−√3/2 because cosine is negative in quadrant II.

The reference angle gives a magnitude, not automatically the sign; tan is undefined where cos is zero.