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

Work with addition and subtraction equations.

Rewrite rational expressions.

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

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Create equations that describe numbers or relationships

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

Generate and analyze patterns.

Gain familiarity with factors and multiples.

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

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Write expressions in equivalent forms to solve problems.

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

Work with radicals and integer exponents.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Represent and solve problems involving multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

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

Solve equations and inequalities in one variable.

Analyze patterns and relationships.

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

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

Write and interpret numerical expressions.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.
problem_activity: Problem 1
Consider the equation
$${ {|x|=5}}$$
.
This can be thought of as a system of equations, where
$${f(x)=\left | x \right |}$$
$${{g(x)}=5}$$
and
$${f(x)={g(x)}}$$
Graph
$${f(x) }$$
and
$${g(x)}$$
in the coordinate plane. Based on the graph, what are the solutions to
$${|x|=5}$$
?
Problem 2
For each absolute value equation below, answer the questions that follow.
$${|x|=-4}$$
$${ |x|=0}$$
$${ |x|=4}$$
How many solutions are there for
$$x$$
in each equation?
Thinking of each equation as two equal functions (similar to Anchor Problem #1), what does each one look like in the coordinate plane? Where do you see the solution(s)?
Problem 3
Solve each absolute value equation algebraically and verify the solution graphically.
$${|x+2|=8}$$
$${|x|+2=8}$$
$${|x+2|+1=0}$$


correct_option_index: 13

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