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.
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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.
At
Rose Training Systems, 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.
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