options: Extend the domain of trigonometric functions using the unit circle.

Interpret expressions for functions in terms of the situation they model.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

Model periodic phenomena with trigonometric functions.

Interpret functions that arise in applications in terms of the context.

Build new functions from existing functions.

Analyze functions using different representations.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.
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.


correct_option_index: 3