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

Generate and analyze patterns.

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

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

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

Solve systems of equations.

Use polynomial identities to solve problems.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Write and interpret numerical expressions.

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

Reason about and solve one-variable equations and inequalities.

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

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

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

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Add and subtract within 20.

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.

Rewrite rational expressions.

Interpret the structure of expressions.

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Problem 1
In equations (a)–(d) below, the solution,
$$x$$
, to the equation depends on the constant,
$$a$$
. Assuming
$$a$$
is positive, what is the effect of increasing
$$a$$
on the solution? Does it increase, decrease, or remain unchanged?
Give a reason for your answer that can be understood without solving the equation.
a.
$$x-a=0$$
b.
$$ax=1$$
c.
$$ax=a$$
d.
$$\frac{x}{a}=1$$
Problem 2
Which of the following equations have the same solution(s)? Give reasons for your answer that do not depend on solving the equations.
a.
$${x+3=5x-4}$$
b.
$${x-3=5x+4}$$
c.
$${2x+8=5x-3}$$
d.
$${10x+6=2x-8}$$
e.
$${10x-8=2x+6}$$


correct_option_index: 22