Sine Cosine Game

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 
   

    
   

_______  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: __________

                      __________




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: __________

                      __________



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

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 _ 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: ____ 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: ____ 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

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 _______ 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: __________ __________ 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: __________ __________ 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

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 _ 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: ____ 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: ____ 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