# Trig Ratios

Consider the following figure:

What values of x, y and z will produce the following inequality?

csc B < sec B < tan B < sin B < cot B < cos B

How does the inequality

sin B < tan B < cos B < cot B < csc B < sec B

change your diagram, values or thinking?

# Trig Functions- Open Middle Problems

Directions: Fill in the empty blanks so that you create a triangle whose Cos Θ = √2/2. You can use whole numbers 1 through 9, but can only use a number once: (5, 4), (__,__) and (__,__)

# Right Triangle Similarity- Open Middle Problem

Directions: Using the numbers 1 to 9 and math operations of (+, -, x, ÷), how many different triangles can you create where tan Θ=.75?

Note: you can only use each number once per triangle created.

# Rectangle Partitions- Open Middle Problem

Directions: Using the numbers 1 to 9, using each number only once, complete the following statement:

___ rows and ___ columns create a rectangle of ___ units

1. What different possibilities will your students come up with?
2. How many of these statements can you create?
3. How would increasing the interval from 1 to 19 change the problem?

# Rectangle Construction- Open Middle Problem

Directions: Using the following squares, how many different rectangles can you make?

How does adding 4 more squares change the problem?

# Shape Partitions- Open Middle Problem

Directions: Using the same cuts, partition these shapes into halves.

Can you expand this to fourths?  Explain why or why not.

Can you create fourths of each picture using unique partitions (no figure is partitioned the same)?  Draw examples and explain why or why not.

# Composite 2D Shapes- Open Middle Problem

Directions: What shapes could be used to create this picture?

Make a list of the shapes needed, and how many of each you would need.

What other pictures could you make with these figures?