Tooling & Production September 2002

"Shop Talk with Steve Rose"


Trigonometry Made Easy
(Part 1)

Trigonometry – one of those multi-syllable math words, like algebra, calculus and statistics. These words strike fear in many hearts.
Fear not! Trig is used every day in the manufacturing environment, helping us calculate part dimensions. On the shop floor the ability to work simple trig problems is a strong advantage when fixing things in a hurry.
Everyone knows "experts", they look at a problem, then disappear to find a computer software package to solve it. Nothing against the computer, but trig can be mastered with a good old calculator and it is easy for us to learn how.
Break down the process into steps and trig becomes a useful and easy tool to use.
Step #1 Draw a 90º triangle, this step is often the most difficult.
Step #2 Label two sides of the triangle, "the known side and the needed side".
Step #3 Select the correct trig rule
Step #4 Calculate the unknown.
Let’s review each step in solving a trig problem.
Step #1 Drawing the triangle.
How do you draw the triangle? This step requires the vision to see where the triangle is on the part.
Trig is often used regularly on turned parts to calculate unknown dimensions. The print does not arrive with the triangle drawn on it, we have to find the triangle.
To find the triangle, always try to read the angle from the horizontal plane. This method helps me when I get confused (often!) about how the print angles should be read.
There are many instances of angles being read incorrectly be the engineer, machinist and then the inspector. When an angle is read incorrectly, there is always one person who will take any and every part we make incorrectly – the scrap dealer. Every one of us keeps the scrap guy in business!
Take a look at this part, the angle as measured from the horizontal is unknown. Trig can be used to calculate this angle. The first step is to draw the right triangle.
Step #2 Labeling two sides of the triangle.

Now that we can see the triangle, label the sides and the angles. The 90º angle is the right angle and is marked with a square. The angle, whose size we wish to calculate is shaded. The third angle is also unknown, but we do not need to calculate this angle, so it is left unmarked.
There are three sides, and three terms that can be applied. The longest side is always the hypotenuse (must be a Greek word, sounds Greek to me). This is always the longest side.

 The next label is "adjacent". This label is applied to the side that is closest to the angle we are calculating. Remember this label with the AA Rule. The angle and the adjacent side always go together ­ the AA Rule.
The third term is "opposite". This label is applied to the side that is opposite the angle we are calculating.
These three terms, opposite, adjacent and hypotenuse represent the lengths of the three sides. When the length values and/or angle values are substituted in the trig formulas, we can calculate the specified unknown.
There are three trig formulas we will use, sine rule, cosine rule and tangent rule. Next month, we will review each in detail and talk about selecting the correct trig rule based on the labeling of the triangle.
Even though we have discussed three sides, we recommend labeling only two sides (the known and the needed). It is then easy to select the correct trig rule and solve the problem.
I’ve created a simple "cheat-sheet" which lists the three main trig rules and their variations. Using this helps to set up the problem and solve the equation. This cheat-sheet is available on our web site at www.rose-training.com. Download the cheat-sheet and check back next month for steps in solving trig problems.