standard_description: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
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