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Numerical Computation
Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.

Measurements
An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.

Trigonometry with Right Triangles
Here we focus on right angle triangles within quadrant I of an xy plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.

Trigonometry with Oblique Triangles
This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.

Vector Analysis

Introduction to Algebra

Factoring

Solving Equations

Functions and Graphs

Geometry
This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.
 Identify, measure, and calculate different types of straight lines and angles
 Calculate the interior angles of polygons
 Solve problems involving a variety of different types of triangles
 Calculate the area of a variety of different types of quadrilaterals
 Solve problems involving circles
 Calculate the areas and volumes of different solids

Introduction to Statistics
Reciprocal Trigonometric Functions
Taking the reciprocal of any value – whether it’s a number, letter, or fraction – means you flip the value over 1. Take for example the number 5. If we flip 5, it becomes a fraction 1/5. 1/5 is the “reciprocal” of 5. How about the fraction 7/8. If we flip 7/8, it becomes 8/7. 8/7 is the “reciprocal” of 7/8. Other examples are shown below:
${x}^{2}\stackrel{\mathrm{reciprocal}\u21f5}{\to}\frac{1}{{x}^{2}}\phantom{\rule{0ex}{0ex}}\u20136\stackrel{\mathrm{reciprocal}\u21f5}{\to}\frac{1}{\u20136}\phantom{\rule{0ex}{0ex}}$ Interestingly, as with all integers including the number 5 and –6 used above, they can be written as fractions. In other words, 5 is the same as 5/1, and –6 is the same as –6/1. This is why when you take their reciprocal, they become the fractions 1 over 5 and 1 over negative 6.
This same principal can be applied to the trigonometric functions learned previously. If we take the reciprocal of each trigonometric function – sin (θ), cos (θ), and tan (θ) – not only are they flipped, they also get a special name and abbreviation:
$\mathrm{sin}\left(\theta \right)\stackrel{\mathrm{reciprocal}\u21f5}{\to}\frac{1}{\mathrm{sin}\left(\theta \right)}=\mathrm{csc}\left(\mathrm{\theta}\right)\left[\mathbf{cosecant}\right]\phantom{\rule{0ex}{0ex}}\mathrm{cos}\left(\mathrm{\theta}\right)\stackrel{\mathrm{reciprocal}\u21f5}{\to}\frac{{\displaystyle 1}}{{\displaystyle \mathrm{sin}\left(\mathrm{\theta}\right)}}=\mathrm{sec}\left(\mathrm{\theta}\right)\left[\mathbf{secant}\right]\phantom{\rule{0ex}{0ex}}\mathrm{tan}\left(\mathrm{\theta}\right)\stackrel{\mathrm{reciprocal}\u21f5}{\to}\frac{{\displaystyle 1}}{{\displaystyle \mathrm{tan}\left(\mathrm{\theta}\right)}}=\mathrm{cot}\left(\mathrm{\theta}\right)\left[\mathbf{cotangent}\right]\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$The unfortunate part about this is that your calculator doesn’t have buttons designated for these reciprocal functions. So when asked to evaluate, let’s say sec (52.1°), you’ll have to remember that secant is 1 over cosine at angle 52.1°:
$\mathrm{sec}\left(52.1\xb0\right)=\frac{1}{\mathrm{cos}(52.1\xb0)}=1.6279\phantom{\rule{0ex}{0ex}}$In other words, you’ll type into your calculator 1 ÷ cos (52.1) to get 1.6279. See if you can evaluate these on your own:
$\mathrm{cot}18.2\xb0\phantom{\rule{0ex}{0ex}}$3.0422
$\mathrm{csc}37.5\xb0\phantom{\rule{0ex}{0ex}}$
1.6426
Sometimes you will be given the ratio (typically as a decimal), and will be asked to find the angle that represents that decimal number. We already know how to do this using ordinary inverse trigonometric function, for example:
$\mathrm{sin}\theta =0.4550\phantom{\rule{0ex}{0ex}}{\mathrm{sin}}^{\u20131}(0.4550)=\theta \phantom{\rule{0ex}{0ex}}\theta =27.06\xb0\phantom{\rule{0ex}{0ex}}$But what about inverse reciprocal trigonometric functions?
To find theta (θ) when given cot θ = 1.7777 or csc θ = 4.2690, your calculator doesn’t have a button designated for the inverse of these reciprocal trigonometric functions either; for example, there’s no cot^{1} or csc^{1}. Hence, you’ll need to remember that each of these equations are equivalent to their reciprocal versions:
$\mathrm{cot}\theta =1.7777\phantom{\rule{0ex}{0ex}}\frac{\mathbf{1}}{\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{}\mathbf{\theta}}=1.7777\phantom{\rule{0ex}{0ex}}\therefore \frac{1}{1.7777}=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}$From the last step, you can easily use your calculator (tan^{1}).
Here’s a video demonstration of a few more examples. You’ll notice that in some examples, the prefix arc is placed in front of csc, sec, and cot. When you see this, it means csc^{1}, sec^{1}, and cot^{1}, respectively. Therefore, arccsc (4.2690) should be treated the same as:
$csc\left(\theta \right)=4.2690\phantom{\rule{0ex}{0ex}}$ In the unit to come, you’ll learn that there’s more to each of these answers. In fact, there are two positive angles between 0° and 360° for every ratio.