# Three New Trig IDs From Similar Right Triangles

- Author:
- Ronan Downes, Tim Brzezinski

- Topic:
- Right Triangles, Triangles

Recall the definitions of the 6 trigonometric functions defined at an angle drawn in standard position within the coordinate plane. (These ratios were defined in terms of

*x*,*y,*&*r*). Interact with this diagram for a minute or two. (The 2 LARGE POINTS are moveable). Then, answer the question prompts that follow.## 1.

Explain why each segment IS what it is. (Some are much easier than others).
For example, how do we know the **purple segment has a length = to the tangent of** ?

## 2.

How many pairs of similar triangles do you see here? How do we know these triangles you reference are all similar to each other?

## 3.

You have previously learned that similar triangles have corresponding sides that are in proportion. That is, ratios of corresponding sides of similar triangles are all equal in value. Given this fact, try to author other trig identities from this picture.