Pre-Calculus: Polar Coordinates, Sequences and Series

A Cartesian coordinate system identifies each point uniquely in a plane by a pair of numerical coordinates and the signed distances from two fixed perpendicular oriented lines, measured in the same unit of length. This course gives you a comprehensive explanation of the concept of the Cartesian coordinate system. It is important to understand how to plot the points on a grid and denote the coordinates using an ordered pair (r, θ). Before working with positive values for the radius and smallest positive angle, it is essential to grasp converting rectangular to polar coordinates. We take you through the different relatable examples of converting rectangular to polar coordinates. We introduce you to the process of changing from a pair of given polar coordinates back to the rectangular equivalent. Have you considered using the formulas required in writing equivalent equations using rectangular coordinates or polar coordinates? We will teach you the formulas you need to transform an equation from rectangular to polar form and vice versa.

This course will demonstrate how to utilise graphing equations in a Cartesian plane and analyse how to graph rational functions. Discover the functions of sequences, elements of series and the steps involved in changing the sequence. Become familiar with the concept of the sigma notation used to write large sums and how to use sigma notation to denote the sum of the first ten squares. Do you know there are sigma laws essential for using sigma notations? We analyse the importance of learning how to manipulate expressions written using sigma notation. We explain how to identify the rules for evaluating limits when combining two functions or raising one function to power or taking a root of that function. If you have struggled with understanding how you can form sums from arithmetic and geometric sequences, then this course is for you!

We will explore the process of finding the limit of a function when looking for trends of functional values presented in a table. We investigate the behaviour of the functional values graph and the function's behaviour by employing a table of values. Learn how to evaluate the limits of the six trigonometric functions as the independent variable approaches a real number. Do you know there are particular circumstances under which an infinite geometric series can also have a sum? This course explores the formulas for the last term of an arithmetic sequence and how to know the numerical value of a sum if the sequence is very short. Discover how you can use limits to calculate an instantaneous rate of change versus an average rate of change. This course will be of great interest to students, researchers and anyone who enjoys learning about pre-calculus concepts. Register for this course and start your next learning experience today!