Unit circle -- more trig than Excel.

[MrShorty]

I recall back when I was first learning trig how much more things made sense once I had a solid grasp of the unit circle. When my oldest child was starting to learn trig, I encouraged her to work hard to understand the unit circle when it came up, and the rest of trig would be a lot easier. It was gratifying when she came back and said that it was true. She struggled with trig until she finally grasped the unit circle.

The attached spreadsheet is a relatively simple attempt to illustrate the unit circle and the basic trig functions. There are four nearly identical sheets. In one sheet, you can enter your angles in degrees, in another, you enter you angles in radians, and in the third, you can enter your angles as mulitples of pi radians (since so much of early trig focuses on "simple" angles like pi*1/3 or pi*3/4 or pi*1). The sheets are protected so someone does not "accidentally" enter an angle in the wrong cell on the wrong spreadsheet, but there is no password if you wish to unprotect it. The fourth tab (angles entered in radians) shows some of the other trig functions (tan, cot, etc.) and how they relate to the unit circle (see Wikipedia for more https://en.wikipedia.org/wiki/Unit_circle ).

I think the main interest for this spreadsheet will be those who are learning or re-learning trig and want to try to understand the unit circle.

For those interested in Excel, it might be a good introduction to how one can draw vectors, or see how to use the trig functions in Excel, or other trig related things.

[Pauleyb]

Worked my eldest through trig last year, but I have two more to go. I agree - I printed out the unit circle for him to help him visualize and see the patterns. I found lots of cheat sheets, but this spreadsheet will be useful for some calculations.
I found this page to have a good summary, and I really liked the "Sin, cos, tan angles values table" (which also includes csc, sec, and cot) towards the bottom of the page.
http://www.ambrsoft.com/Equations/Tr...igonometry.htm

[MrShorty]

I don't know if this will add clarification or confusion to this. shg's post in this thread: http://www.excelforum.com/excel-form...ml#post4308986 Caused me to look at this again and adapt the concept of the unit circle to compass bearings.

In dealing with angles, there are two common conventions.
1) The standard convention we learn in trig, where angles are referenced to the positive x axis, and angles increase in a CCW direction. This is the convention illustrated in the first spreadsheet. Under this convention, cos(theta) represents the x coordinate, sin(theta) represents the y coordinate, and other trig functions as illustrated.
2) With compass bearings, we have a different convention. Angles are referenced to the positive y axis (North), and angles increase in a CW direction. What shg's post helped me see is that, under this convention, the x coordinate corresponds to sin(theta) and the y coordinate is now cos(theta), adjusting the meanings of the other trig functions accordingly. I have illustrated this in the spreadsheet attached to this post.

I think this will either create confusion, as people may have trouble keeping the two conventions separate. Or, it will help those who need to work with compass bearings to better understand the trig functions they need to work with those angles. I am hoping the latter will be the case.

[LonnieLSmith]

That is a very slick page, but I am not sure how to make it work for what I need. Currently, I have 3 calculations I need. Please find the attached and see if you can help me with the formulas. The ones still in question are highlighted in yellow.

Heliocentric Model Calculations (7-13-2016).xlsx

[MrShorty]

For future searchers interested in Lonnie's specific question, we discussed it in some detail here: http://www.excelforum.com/excel-form...d-degrees.html