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:
{
  "explanation": "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: Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Interpret the structure of expressions.

Solve systems of equations.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Use properties of operations to generate equivalent expressions.

Work with equal groups of objects to gain foundations for multiplication.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Rewrite rational expressions.

Understand the connections between proportional relationships, lines, and linear equations.

Solve equations and inequalities in one variable.

Understand solving equations as a process of reasoning and explain the reasoning.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Understand and apply properties of operations and the relationship between addition and subtraction.

Analyze patterns and relationships.

Understand properties of multiplication and the relationship between multiplication and division.

Work with addition and subtraction equations.

Write and interpret numerical expressions.
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: 19