Trigonometric properties: demonstrative model
Objective and steps
Trigonometric ratios and functions satisfy many interesting properties. Let us find some of them. We will use a geometric structure to visualize the triangles involved.
Students work in pairs (A and B).
1) Student A selects a value for the acute angle in the green triangle, (this value must be acute, otherwise, disfigures the geometric structure).
2) Student B selects a position for the orange point.
Observe that in the geometric structure:
- The acute angle in the yellow triangle is always equal to the green value.
- All triangles are square.
- Hypotenuse in the red triangle is unitary.
- Control boxes show hints about equalities on lengths.
3) By turns, students A and B complete all missing symbolic informationin the spreadsheet (remember to write all information using “quotation marks”). Use expressions such as: , , , , , .
4) Students write down conclusions about the observed algebraic equalities.