Trigonometry Made Easy
We’ve been discussing trigonometry.
Trig can be easy when you break it down and follow the steps
outlined here.
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| 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. |
The only step left is to solve the problem.
This is the part we’ve been using.
In last month’s issue the triangle was labeled as shown.
With the sides labeled opposite and adjacent, the tangent rule was selected.
tangent rule tangent of the angle = side opposite ÷ side adjacent
To solve the problem, simply replace the words with the value of the side of the triangle.
Tangent rule tangent of the angle = 0.876 ÷ 1.2510
Use the calculator’s 2nd function to determine the size of the angle. (Your calculator may operate differently, but many operate by using the following sequence. 0.7002
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The use of the tangent rule allows us to
calculate the size of the angle. For this part, the angle is
34.9997º.
Follow these four steps and you can solve
most all machine shop trig problems.
In our business, we analyze prints and use trig to calculate part
dimensions in an effort to program the part.
Sometimes the process is reversed.
Here’s a twist on the trig process. Here
is a program to turn the profile of the part shown. Use the program
to calculate the size of each angle.
| Part Program | |
| G00 X0.900 Z0.050 ; | (start ) |
| G01 Z0. F0.008 ; | ( blend face ) |
| X1.0637 | ( first chamfer start ) |
| X1.2000 Z-0.0682 | ( cut chamfer ) |
| Z-0.2851 | ( start angle A ) |
| X1.000 Z-0.6583 | ( plunge angle A ) |
| Z-1.8341 | ( turn 1.0 dia. ) |
| X1.5753 Z-2.3750 | ( turn angle B ) |
| X2.800 | ( face up ) |
