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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
Writing Sinusoidal Equations without a Graph
Oftentimes you’ll be presented with the properties of the wave and will be expected to create an equation from them. For example, you may be given the amplitude, period, phase-shift or told that it reflects about the x axis or has a height of n. Whatever the case is, you always start one of the general formulas:
- y = a⋅sin(bx + c) + d
- y = a⋅cos(bx + c) + d
Some general tips to follow:
- If given the amplitude or height, begin by filling in the factor a first.
- If given the period and phase-shift, you need to find the value b using the period before you can find the value for c.
- If the period and phase-shift is given without units (such as degrees °), the equation is in radians.
- Always have a summary of the formulas ready or memorized: