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After I introduce my students to the sine and cosine functions, I
begin a class period with the following game that has proved quite
successful. First I divide the class into pairs and distribute single
sheets of paper to each pair. On this sheet are two columns. The
left-hand column contains expressions involving either the sine or
cosine function. In the right-hand column are actual decimal
approximations of the expressions in the left-hand column,
but in a random order. The values are chosen such that only one of the
five decimal values is plausible for each function.
At the signal from me, each pair has three minutes to match each expression in the left-hand column with its proper decimal representation in the right-hand column. Calculators are not permitted. Any pair is a winner if it obtains all five correct matchings. After I have introduced all six trigonometric functions, I play the same game but mix secant with cosine or cosecant with sine expressions in the left-hand column. The game can be made even more challenging by using more trigonometric expressions in this column. However, ambiguities are more likely to occur, so care must be taken. Students have responded very well to this exercise. It especially reinforces those skills involving deductive reasoning, graph interpretation, and approximation. Finally, students are given an opportunity to learn from, and work with, each other. |
Precalculus Names: ____________________________________
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Matching #1
_______ cos 35 A. -0.9961 _______ cos 98 B. 0.8192 _______ cos 4 C. 0.0349 _______ cos 175 D. -0.1391 _______ cos 272 E. 0.9976
Precalculus Names: ____________________________________
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Matching #2
_______ sin 224 A. 0.1908 _______ sin 52 B. 0.7888 _______ sin 290 C. -0.0871 _______ sin 355 D. -0.6946 _______ sin 11 E. -0.9396
Precalculus Names: ____________________________________
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Matching #3
_______ cos 7 A. -1.2360 _______ sec 98 B. 1.0456 _______ cos 304 C. 0.5591 _______ sec 17 D. -7.1852 _______ sec 144 E. 0.9925
Precalculus Names: ____________________________________
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Matching #4
_______ csc 130 A. -28.653 _______ sin 289 B. 1.3054 _______ sin 185 C. -1.0402 _______ csc 254 D. -0.9455 _______ csc 358 E. -0.0871