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The sine

 

 

 

Graph

function

number of loops

 

 

 

sin q

1

sin 2q

4

sin 3q

3

sin 4q

8

sin 5q

5

sin 6q

12

sin 7q

7

sin 8q

16

sin 9q

9

sin 10q

20

sin 11q

11

sin 12q

24

sin 13q

13

sin 14q

28

sin 15q

15

sin 16q

32

sin 17q

17

sin 18q

36

sin 19q

19

sin 20q

40

sin 21q

21

sin 22q

44

sin 23q

23

sin 24q

48? Does this follow the pattern?

This one was quite strange; it did not fit within the normal viewing window. See its viewing window here.

sin 25q

23

sin 26q

44

sin 27q

21

sin 28q

40

sin 29q

19

sin 30q

36

sin 31q

17

sin 32q

32

sin 33q

15

sin 34q

28

sin 35q

13

sin 36q

24

sin 37q

11

sin 38q

20

sin 39q

9

sin 40q

16

sin 41q

7

sin 42q

12

sin 43q

5

sin 44q

8

sin 45q

3

sin 46q

4

sin 47q

1

sin 48q

0? For the cosine, this graph is the unit circle.

This one, like 24, did not fit into the standard viewing window.

sin 49q

1

Observation: 49 is equal to 47 flipped about the x-axis.

sin 50q

4

This is a repeat of 46. Another cycle is beginning, although now, everything is reflected about the x-axis.

 

 

 

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