Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make the trigonometric equation below true:
Hint
Which radian angles result in sine values that are integers?
Answer
There are many possible answers (see image). The denominator must be an even number.
Extension: If the last box must be a 9, how does that change your solutions?
Extension: If the last box must be a 9, how does that change your solutions?
Source: Kevin Rees
I am not sure if here is an appropriate place for correct answers, but here are some other combinations my students found, starting from the blank on the left and working to the blank on the right:
9, 4, 6, 3, 2 ,7
5, 4, 6, 7, 2, 3
5, 1, 2, 9, 8, 4
5, 3, 4, 9, 7, 2
5, 3, 4, 8, 6, 2
6, 1, 2, 4, 3, 5
6, 1, 2, 8, 7, 5
6, 1, 2, 9, 8, 5
4, 3, 2, 9, 8, 1
Here are some more:
3, 1, 2, 8, 9, 4
9, 4, 2, 8, 7, 5
5, 4, 6, 2, 1, 3
9, 1, 2, 4, 3, 8
4, 2, 6, 8, 7, 3
3, 1, 6, 8, 5, 2
9, 4, 2, 7, 6, 5
7, 1, 2, 9, 8, 6
7, 3, 2, 9, 8, 4
9, 6, 2, 5, 4, 3
5, 4, 6, 7, 2, 3
And finally…
3, 4, 6, 9, 8, 1
4, 3, 6, 9, 8, 3
9, 8, 6, 7, 2, 5
8, 2, 4, 5, 3, 6
8, 2, 6, 5, 4, 7
3, 2, 6, 7, 4, 1
4, 2, 6, 3, 8, 5