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

Understand and apply the Pythagorean Theorem.

Understand congruence in terms of rigid motions.

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

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

Prove theorems involving similarity.

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

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

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Apply trigonometry to general triangles.

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

Understand similarity in terms of similarity transformations.

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

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

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

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

Analyze, compare, create, and compose shapes.

Understand and apply theorems about circles.

Make geometric constructions.

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

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

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

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Narrative
In this activity, students identify and sketch angles in their environment—in the text, graphics, and shapes in their physical surroundings—and reinforce the idea of an angle as a figure made up of two rays that share an endpoint.
In future lessons, students will look more closely at the properties of angles and consider how they can be measured and whether the length of the segments that form them impacts the size of the angles.
Required Materials
Materials to Gather
Rulers or straightedges
Launch
Groups of 2
Give each student a ruler or a straightedge.
Activity
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Here are two figures.
[IMG]
Find 2–3 angles in each figure. Draw pairs of rays to show the angles.
Sketch a part of your classroom that has 2–3 angles. Draw pairs of rays to show the angles.
Student Response
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for free access to Student Response.
Advancing Student Thinking
Students may say they have identified an angle because they have found a vertex. Ask these students to explain what they mean and to describe the angle they see. Consider asking:
“How do you see the rays that share this vertex? Can you draw them?”
“Could more than one angle share a vertex? How could you use figure A from the previous activity to explain?”
Activity Synthesis
“How did you find the angles?” (We looked for intersections of segments. When the segments meet or cross, angles are formed.)
“Where is the vertex of each angle you found?”


correct_option_index: 11