Trig Functions Summary

Pre-Calculus · Axiom Academy

SUMMARY Trigonometric Functions A complete review of angles, the unit circle, the six functions, right-triangle trig, and their applications. An angle in standard position has its vertex at the origin and initial side on the positive x -axis; coterminal angles differ by a full turn ( or ). Convert degrees to radians by multiplying by , and radians to degrees by multiplying by . On the unit circle , the point at angle is — so is the x -coordinate and is the y -coordinate. The reference angle plus the quadrant (via ASTC ) gives every trig value; SOH-CAH-TOA ties the same ratios to right triangles. Core Concept Angles & Standard Position An angle is in standard position when its vertex sits at the origin and its initial side lies along the positive x -axis. Positive angles open counterclockwise, negative ones clockwise. Coterminal: add or subtract (or ) to land on the same terminal side. Watch out for: there are infinitely many coterminal angles for any direction. Core Concept Degrees & Radians Two units measure the same angle. A full circle is radians, so a half circle is radians. When to use: radians for calculus and the unit circle; degrees for everyday geometry. Watch out for: keep exact instead of rounding too early. On a circle of radius 1 , the terminal side meets the circle at . This extends sine and cosine to every angle, not just acute ones. (the height) and (the horizontal). Watch out for: cosine comes first in the ordered pair, sine second.

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