This math unit begins by developing a foundational understanding of trigonometric functions through the use of the unit circle, focusing initially on calculating sine and cosine values of angles in both radians and degrees. The unit progresses to applications involving the identification of trigonometric angles and their positioning in different quadrants using visual representations and radian measures. Students advance to associating trigonometric ratios with their signs in various quadrants and understanding quadrant-related trigonometric identities. Midway through the unit, the focus shifts to deeper explorations of trigonometric identities involving negative angles and specific calculations in 30-60-90 triangles using the Pythagorean theorem. The latter portion of the unit introduces more complex concepts, such as identifying trigonometric ratios (tangent, secant, cosecant, and cotangent) from unit circle coordinates and recognizing reciprocal relationships between these ratios. The unit culminates in mastering the Pythagorean identity within the unit circle context, enabling students to solve for X and Y dimensions based on trigonometric concepts, enhancing both their analytic skills in geometry and their proficiency with trigonometric identities. Through these sequential topics, students build a comprehensive understanding of trigonometry, from basic unit circle knowledge to advanced applications involving identities and geometric relationships.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.