# New Trig IDs From Similar Right Triangles

- Author:
- Tim Brzezinski, Steve Phelps

- 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.* You can type them in the space below. Or, even better, feel free to type or use the digital pen to write them in the app below this space.