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Trigonometry made easy, part 3.

We've been discussing trigonometry. Trig can be easy when you break it down and follow the steps outlined here.

Step #1: Draw a 90[degrees] 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.

Over the past few months we've reviewed drawing a 90[degrees] triangle. We've labeled only two sides of the triangle and selected the correct trig rule based on the two labeled sides.

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

Perform the mathematical function.

Tangent of the angle = 0.7002

Use the calculator's second function to determine the size of the angle. Your calculator may operate differently, but many operate by using the following sequence.

The use of the tangent rule allows us to calculate the size of the angle. For this part, the angle is 34.9997[degrees]. Follow these four steps and you can solve most 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)

Remember to work step-by-step for each angle using the four steps shown above. Check our website for the results ( Good luck!

Steve Rose is a professional trainer and president of RTSI, Solon, OH. Rosaleen Rose offers Internet website development. They can be reached by phone, 440.542.3066; e-mail; or on the web at
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Title Annotation:T&P shop talk
Author:Rose, Steve
Publication:Tooling & Production
Geographic Code:1USA
Date:Dec 1, 2005
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