MAC1114

The student will utilize both degree/minute/second and radian measurement frameworks to describe angles and demonstrate facility in converting one to the other.

The student will utilize these measures to quantify sector areas, arc lengths, and linear and angular velocities of objects in circular motion.

The student will evaluate the six basic trigonometric functions, both in the context of right triangles and the unit circle, and apply these to solve applied problems involving distance, time, and area.

The student will develop important properties of these trigonometric functions and use them to construct their graphs, illustrating period, amplitude, and phase shift.

The student will justify the equivalence of trigonometric expressions using learned identities and formulas, utilizing these and other algebraic techniques to solve trigonometric equations.

The student will develop and examine the inverses of trigonometric functions and use them in solving equations.

The student will use various applications of trigonometric functions to solve triangles, including the Laws of Sines and Cosines, sum and difference formulas, double- and half-angle formulas, and triangle area formulas.

The student will examine the relationships between planar rectangular and polar coordinate systems, converting between these as needed, and define and illustrate trigonometric functions.

The student will represent complex numbers in their rectangular, polar, and exponential forms and use DeMoivre’s Theorem to calculate powers and roots.

The student will explore the usefulness of vectors as a means of describing position, magnitude, and motion and learn to combine vectors using addition, subtraction, scalar multiplication, and dot-product multiplication.

The student will also model linear and curvilinear motion in a plane using parametric equations.