This math unit provides a comprehensive exploration of trigonometric identities within the framework of the unit circle, transitioning from basic understanding to complex application across various trigonometric functions. It begins with establishing the foundational understanding of Pythagorean identities using degrees and radians, focusing on the identities of sine and cosine functions. Students then extend this knowledge to understand and apply these identities in the context of negative angles and radians, reinforcing symmetry properties of the trigonometric functions. Progressing into more advanced topics, the unit explores the behavior of trigonometric ratios in different quadrants of the unit circle, enhancing students’ capability to determine the signs and values of sine, cosine, and tangent depending on the quadrant. This culminates with applying these quadrant-based understandings to specify angles and positions within the unit circle. Further, the unit delves into more specific trigonometric identities involving reciprocal relationships, double angles, half angles, and cofunctions. Students are required to manipulate and transform these identities in radians and degrees, facilitating a deeper grasp of how trigonometric functions interrelate and apply in various mathematical contexts. The sequence from basic identities to complex manipulations enables a graduated learning curve, building proficiency in trigonometric calculations and their applications.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.