# Mathematics for Technology I (Math 1131) Durham College, Mathematics
Free • 0 lessons
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• 10 week duration
• ##### 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 x-y 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.

• ##### Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

## Mathematics for Technology I (Math 1131)

### 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:

• 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:

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°:

$\mathrm{sec}\left(52.1°\right)=\frac{1}{\mathrm{cos}\left(52.1°\right)}=1.6279\phantom{\rule{0ex}{0ex}}$

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:

3.0422

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1.6426

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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:

### 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:

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-1sec-1, and cot-1, respectively. Therefore, arccsc (4.2690) should be treated the same as: