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: Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Reason with shapes and their attributes.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Analyze, compare, create, and compose shapes.

Understand congruence in terms of rigid motions.

Translate between the geometric description and the equation for a conic section.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

Visualize relationships between two-dimensional and three-dimensional objects.

Explain volume formulas and use them to solve problems.

Classify two-dimensional figures into categories based on their properties.

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

Apply geometric concepts in modeling situations.

Experiment with transformations in the plane.

Solve real-world and mathematical problems involving area, surface area, and volume.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Prove geometric theorems.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Apply trigonometry to general triangles.
problem_activity: A family has a house on a plot of land and would like to build an addition. The map below shows the “footprint” of the original house, the proposed addition, and the family’s plot of land. Each grid line represents 10 linear feet.
[IMG]
The family’s plot of land is rectangular. What are the values of the missing coordinates,
$$x$$
and
$$y$$
?
What is the ratio of the proposed addition “footprint” area to the original house “footprint” area?
What is the area of land that will not have a building on it if the proposed addition is approved and built?
Prove that the proposed addition “footprint” is a right triangle.


correct_option_index: 14