Constructing Trigonometric Substitution Triangles

The process to create the triangle used for trigonometric substitution from one of 3 given equations:

• $\sqrt{a^2-x^2}$
• $\sqrt{a^2+x^2}$
• $\sqrt{x^2-a^2}$

1. Create a right-angle triangle with $\theta$ as the acute angle
2. Given your equation, determine if its the hypoteneuse or if its a side
3. Then, you want to choose which sides $a$ and $x$ are. You want to get a relationship s.t $\frac{x}{a}$ is tan, sin or sec