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, in json format:
{
  "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: Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

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

Write and interpret numerical expressions.

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

Solve equations and inequalities in one variable.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

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

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

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

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

Analyze patterns and relationships.

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

Understand the relationship between zeros and factors of polynomials.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

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

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

Use polynomial identities to solve problems.

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

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.
problem_activity: Given below are the graphs of two lines,
$${y = 0.5x + 5}$$
and
$${y = -1.25x + 8}$$
, and several regions and points are shown. Note that C is the region that appears completely white in the graph.
[IMG]
For each region and point, write a system of equations or inequalities that has the region or point as its solution set.
Verify that a point that lies in region A satisfies the system of inequalities that you wrote for region A.
Without choosing any specific numbers, explain how you know that all the points in quadrant 3 must satisfy the inequalities for region A.


correct_option_index: 3

4