Trigonometry Challenges

1. Can you find two linear functions f(x) and g(x) such that the lines are tangent to the graph of k(x) which is the quadratic expression that is the product of the linear expressions of f(x) and g(x)?

2. If 12 oxen eat up three and one-third acres of pasture in 4 weeks and 21 oxen eat up 10 acres in 9 weeks, how many oxen will it take to eat up 24 acres in 18 weeks?

3. A bridge 5280 feet long was built with expansion joints omitted. When the bridge expands with the heat and "bows", will the bow be visible when the bridge expands two feet?

4. A rectangle is cut by an arc. Where could the arc be in order to divide the rectangle into two equal areas?

5. A box can be made by cutting squares from the corners of an 11 x 14 inch sheet of paper and then folding up the sides and taping the edges together. What would be the dimensions of the square that would result in a box having maximum area?