IM3.6.5 Tangent 1
Task 1: Similar Triangles
Trigonometric ratios are built on side ratios of similar triangles. We're going to use similar triangles to define tangent on the unit circle.
Find the sides
In the diagram above, right triangle AB'D has altitude B'C. Find the exact values of each of the following. a. AD b. DB' c. B'A d. AC e. B'C
Ratios
Answer the following by writing fractions comparing segments from the diagram (for example, ) 1. What ratio is equal to the sine of angle AB'C? 2. What ratio is equal to the cosine of angle AB'C? 3. What ratio is equal to the tangent of angle AB'C? 4. Using the fact that AB'D~ACB' to write a ratio from AB'D equal to your answer for number 3.