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: Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

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

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

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

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

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

Analyze patterns and relationships.

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

Write expressions in equivalent forms to solve problems.

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

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

Multiply and divide within 100.

Use polynomial identities to solve problems.

Add and subtract within 20.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

Interpret the structure of expressions.

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

Rewrite rational expressions.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

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

Reason about and solve one-variable equations and inequalities.

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

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.
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: 0

25