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Yang Kuang
Articles & Books From Yang Kuang
Article / Updated 02-20-2019
Every good thing must come to an end, and for pre-calculus, the end is actually the beginning — the beginning of calculus. Calculus includes the study of change and rates of change (not to mention a big change for you!). Before calculus, everything was usually static (stationary or motionless), but calculus shows you that things can be different over time.
Article / Updated 02-20-2019
Functions can be categorized in many different ways. Here, you see functions in terms of the operations being performed. Here, though, you see classifications that work for all the many types of functions. If you know that a function is even or odd or one-to-one, then you know how the function can be applied and whether it can be used as a model in a particular situation.
Article / Updated 08-14-2023
As you work through pre-calculus, adopting certain tasks as habits can help prepare your brain to tackle your next challenge: calculus. In this article, you find ten habits that should be a part of your daily math arsenal. Perhaps you’ve been told to perform some of these tasks since elementary school — such as showing all your work — but other tricks may be new to you.
Step by Step / Updated 02-20-2019
Here you find some pretty amazing curves that are formed from some pretty simple function equations. The trick to drawing these polar curves is to use radian measures for the input variables and put the results into a polar graph. A polar graph uses angles in standard positions and radii of circles; it’s not your usual rectangular coordinate system.
Cheat Sheet / Updated 07-24-2021
When you study pre-calculus, you are crossing the bridge from algebra II to Calculus. Pre-calculus involves graphing, dealing with angles and geometric shapes such as circles and triangles, and finding absolute values. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations.
Article / Updated 07-08-2021
In Pre-Calculus, you're going to come across triangles with right angles that vary in degree. This article covers two of the most common right triangles you'll find.
45-45-90 degree triangles
All 45-45-90-degree triangles (also known as 45ers) have sides that are in a unique ratio. The two legs are the exact same length, and the hypotenuse is that length times the square root of 2.
Article / Updated 07-25-2019
Of course you use trigonometry, commonly called trig, in pre-calculus. And you use trig identities as constants throughout an equation to help you solve problems. The always-true, never-changing trig identities are grouped by subject in the following lists:
Article / Updated 03-26-2016
Three trigonometric ratios — secant, cosecant, and cotangent — are called reciprocal functions because they're the reciprocals of sine, cosine, and tangent. These three functions open up three more ways in which you can solve equations in pre-calculus. The following list breaks down these functions and how you use them:
Cosecant, or
is the reciprocal of sine.
Article / Updated 03-26-2016
Although it may seem daunting, graphing polynomials is a pretty straightforward process. Once you have found the zeros for a polynomial, you can follow a few simple steps to graph it.
For example, if you have found the zeros for the polynomial f(x) = 2x4 – 9x3 – 21x2 + 88x + 48, you can apply your results to graph the polynomial, as follows:
Plot the x- and y-intercepts on the coordinate plane.
Article / Updated 07-08-2021
Gaussian elimination is probably the best method for solving systems of equations if you don't have a graphing calculator or computer program to help you.The goals of Gaussian elimination are to make the upper-left corner element a 1, use elementary row operations to get 0s in all positions underneath that first 1, get 1s for leading coefficients in every row diagonally from the upper-left to the lower-right corner, and get 0s beneath all leading coefficients.