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

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

Explain volume formulas and use them to solve problems.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

Experiment with transformations in the plane.

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

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

Understand congruence in terms of rigid motions.

Find arc lengths and areas of sectors of circles.

Reason with shapes and their attributes.

Understand similarity in terms of similarity transformations.

Make geometric constructions.

Apply trigonometry to general triangles.

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

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

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

Use coordinates to prove simple geometric theorems algebraically.

Prove theorems involving similarity.

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

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

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

Prove geometric theorems.
problem_activity: Task
A square is inscribed in a circle which is inscribed in a square as shown below. Note that the vertices of the inner square meet the midpoints of the outer square's sides.
[IMG]
Consider the area of the region left by removing the interior of the small square from the interior of the big square. Is the area of the blue region more or less than $\frac12$ of that?


correct_option_index: 19

23