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

Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

Analyze functions using different representations.

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

Construct and compare linear and exponential models and solve problems.

Use functions to model relationships between quantities.

Define, evaluate, and compare functions.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

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

Build new functions from existing functions.
problem_activity: Task
Below are pictures of the first three  triangular numbers:
[IMG]
In general, the $n^{\text{th}}$ triangular number is the total number of dots in $n$ columns where the columns have $1, 2, 3, \ldots, n$ dots.
The following picture relates the first three triangular numbers to areas of rectangles:
[IMG]
Use this idea to calculate the seventh triangular number, $1 + 2 + 3 + 4 + 5+ 6+ 7$.
Calculate the hundredth triangular number, $1 + 2 + 3 + \cdots + 98 + 99 + 100$.
Find a formula for calculating the $n^{\text{th}}$ triangular number, $1 + 2 + \cdots + (n-1) + n.$


correct_option_index: 5