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Triangles, The Unit Circle and Radians

The Unit Circle and Radian Measurement of Angles

The Unit Circle and
Radian Measurement of Angles

This is the last of the basic math posts for awhile. The next posts will be about creating a flotation platform that can be used as a raft or floating dock.  We will be using much of this math.  This one is based around a video like the previous ones.

There are several points I wanted to introduce in this video.

First, the internal angles in all triangles sum up to 180 degrees.  That creates a special term in right triangles.  Because one of the angles is known to be 90 degrees in a right triangle the other two angles must sum up to be 90 degrees.   Once one of those angles is known the new term for tonight is the other angle is called the complementary angle.

The next point I want to drive home is that any triangle can be made into two right triangles.  This is often helpful to solve problems that could not be solved otherwise using the powerful tool we have learned with trigonometry.

Spreadsheet showing several problems with trigonometry with programs.

Spreadsheet showing several problems with trigonometry with programs.

Next I show how the concept of a unit circle can be used to extend trigonometry past a right triangle. This is done by declaring that radius X sine value represents the Y axis value and radius X cosine value represents the X axis value of a point.

Next I show an angle measurement called radians. Radians is not exactly human friendly, because we have all used degrees to measure angles. However it is necessary to become familiar with the term because most computer programs including spreadsheets use radians instead of degrees when calculating the trig. functions.

Finally, I use a spreadsheet to show that when using a computer program with the inverse trig functions (i.e. arcsine, arc-cosine, etc.) it is necessary to always keep your head in the game because the functions only report the answer in two quadrants.

The associated video is below.

As always I hope this is helpful to you.  There is quite a bit being thrown out tonight and I may have not been 100% clear.  If you have any questions, please feel free to e-mail me.

Gary

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