options: Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Use functions to model relationships between quantities.

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

Extend the domain of trigonometric functions using the unit circle.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Build a function that models a relationship between two quantities.

Interpret expressions for functions in terms of the situation they model.
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: 8