Trig+Lab

**Trigonometry Calculator Lab:**
See a link to the Calculator Lab 1 we did in class with guiding questions. We filled in this excel file with the results gathered from the Calculator lab. [|ti-83] After the calculator lab, we went through a discussion in class where we color-coded the //related angles// (ie. 30, 150, 210, 330) and connected it to the Unit Circle.

Extension: Calculator Lab 2 Use to explore negative angles and their relationships to the related angles already found.

We also discussed the domain and range of sin, cos, and tan functions (note: the sine and cosine values are between -1 and 1). Students recognized from the data that the tangent function was not like the sine and cosine in that it's value could be greater than one. Once they discovered this important concept, we explored the value of the tangent function for angles very close to 90 and 270 (ie. 89.95) and were able to see quickly that tangent ratio value became very large.

The Excel sheet allowed the students to see on one page the values for each ratio and the patterns (we were able to determine from this exercise the signs of sin, cos, tan in the I, II, III and IV quadrants)

SinCosTan is a spreadsheet that graphs the Sine, Cosine, Tangent curves using a scatter plot. I also included some guiding questions on this spreadsheet.

I created the graph ahead of time and then deleted the values in the table so that the graph would be drawn as the students entered in values.

1) can be used to show degrees converted to radians (*this is sometimes a difficult concept for students - the spreadsheet made it more accessible and the students didn't think it "was so bad." :)

2) when entered into Excel, tan 90 and tan 270 result in the ######### (this is an asymptote line - zero in the denominator error on calculator) - have students explore the tangent of 89 degrees, 89.5 degrees, 89.999 degrees (values continue to get bigger and bigger)

3) analyze the results and ask what the minimum and maximum values of sine, cosine and tangent be? (range)

//Use this interactive spreadsheet (with slider!) created by Wendy Petti,// http://mathcats.com/spreadsheets/
 * [[image:2010-04-20_2151.png width="469" height="300" align="right" link="@http://www.box.net/shared/zpuhd6u771"]]Extension:** Graph the translations like y=3 sin x (height will change to +3 and -3) and y=sin 3x (3 full sine graphs will be displayed between 0 to 360).

Note: in this example, the angles are in radians. Students will need help recognizing that 360 degrees is the same as 6.28 radians (2pi).

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