A trigonometry course explores the relationships between angles and sides in triangles, with a strong emphasis on right triangles and the unit circle. Students learn the primary trigonometric ratios—sine, cosine, and tangent—and how to apply them to solve problems involving angles and distances. The course also introduces reciprocal functions (cosecant, secant, and cotangent), as well as concepts like radians, angular velocity, and inverse trig functions. Trigonometric identities, such as the Pythagorean identity and angle sum formulas, play a central role in simplifying expressions and solving equations.
Beyond triangles, trigonometry extends to modeling periodic phenomena such as sound waves and circular motion, using sine and cosine functions. Students learn to graph these functions and analyze key features like amplitude, period, phase shift, and vertical shift. The course often integrates algebraic skills, especially when manipulating equations or verifying identities. Overall, trigonometry provides critical tools for understanding patterns and changes in both pure and applied math contexts, laying the groundwork for further study in precalculus, physics, and engineering.