few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

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

Use functions to model relationships between quantities.

Define, evaluate, and compare functions.

Prove and apply trigonometric identities.

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Build a function that models a relationship between two quantities.

Interpret functions that arise in applications in terms of the context.
problem_activity: When Janaya started working, she researched how income tax was determined. She read that income up to and including $10,000 is taxed at a rate of 10%. Any income over $10,000 and up to and including $40,000 is taxed at a rate of 15%. For example, if Janaya earned $11,000 in one year, the first $10,000 would be taxed at a rate of 10% and the last $1,000 would be taxed at a rate of 15%.
How much income tax would Janaya pay if she earned $15,000 in one year?
Write a piecewise function to represent the situation.
How much more income tax would a person who earns $30,000 pay than a person who earns $10,000 in one year?


correct_option_index: 11