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 congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

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

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

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

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

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

Explain volume formulas and use them to solve problems.

Apply trigonometry to general triangles.

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

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

Understand similarity in terms of similarity transformations.

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

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

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

Find arc lengths and areas of sectors of circles.

Understand and apply theorems about circles.

Make geometric constructions.

Prove theorems involving similarity.

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

Experiment with transformations in the plane.

Apply geometric concepts in modeling situations.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
problem_activity: Task
Lisa makes an octagon by successively folding a square piece of paper as follows.  First, she folds the square in half vertically and horizontally and also along both diagonals leaving these creases:
[IMG]
Next, Lisa makes four more folds, identifying each pair of adjacent lines of symmetry for the square used for the folds in the first step:
[IMG]
Finally Lisa folds the four corners of her shape along the red creases marked below:
[IMG]
Explain why the shape Lisa has made is a regular octagon.


correct_option_index: 21

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