standard_description: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
problem_activity: Task
[IMG]
In the triangle pictured above show that
$$
\left(\frac{|AB|}{|AC|}\right)^2 + \left(\frac{|BC|}{|AC|}\right)^2 = 1
$$
Deduce that $\sin^2{\theta} + \cos^2{\theta} = 1$ for any acute angle $\theta$.
If $\theta$ is in the second quadrant and $\sin{\theta} = \frac{8}{17}$ what can you say about  $\cos{\theta}$?  Draw a picture and explain.


aligns: no