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: ____________________________________ ____________________________________ 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: ____________________________________ ____________________________________ Matching #2
Precalculus Names: ____________________________________ ____________________________________ Matching #3
Precalculus Names: ____________________________________ ____________________________________ Matching #4