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- 14 week duration
Solving Systems of Equations
This unit introduces how to systematically solve a system of equations, namely linear equations. Examples of non-linear systems, including systems of 3 unknowns will be of emphasis.
Graphs of Trigonometric Functions
The unit focuses primarily on how to graph periodic sinusoidal functions, and how to identify features of a waveform to produce an equation by inspection.
Polar Coordinate Functions
An introduction to the polar coordinate system.
Exponents and Radicals
This unit is an extension of what was introduced in Math 1131. To learn how to work with radicals, knowing your exponent laws in crucial. Hence, this unit begins with a thorough review.
This chapter introduces you to exponential functions, and how they can be solved using logarithms.
Trigonometric Identities and Equations
Graphing Polar Equations on a Polar Plane
In the first lesson of this unit, you were lightly introduced to graphing polar coordinates. This lesson revisits what you learned earlier, and extends those ideas to graphing polar equations.
In the first of three videos below, you will learn how to graph polar coordinates with negative values, namely when:
- the angle is negative
- the radius is negative
- both properties are negative
You’ll discover that when the angle is negative angle, the terminal side moves clockwise from the polar axis, and vice versa for when its positive. In addition, a negative radius gives a direction of the terminal side opposite to the angle.
Perhaps the greatest challenge to this section comes when graphing polar equations. Generally, graphing polar equations isn’t an easy task, and depending on your level of study, it can quite complicated when taking into account symmetry. Luckily, our analyse won’t exceed what we already know about negative/positive angles and radii. Starting with the first video, you’ll graph two trigonometric equations – one that’s in degrees and the other that’s in radians. To find the polar coordinates of an equation, you’ll create a table of values using angles from θ = 0° to 360°. Recall that a point with a radius of (−r) is plotted in the opposite direction to (+r).
Sometimes a polar equation can be written as a pair of parametric rectangular equations. If you encounter a question like that, one major thing to keep in mind is to follow the previous point when connecting to form your curve.