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 similarity in terms of similarity transformations.

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

Analyze, compare, create, and compose shapes.

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

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

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

Use coordinates to prove simple geometric theorems algebraically.

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

Define trigonometric ratios and solve problems involving right triangles.

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

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

Understand congruence in terms of rigid motions.

Prove theorems involving similarity.

Experiment with transformations in the plane.

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

Find arc lengths and areas of sectors of circles.

Explain volume formulas and use them to solve problems.

Prove geometric theorems.

Understand and apply theorems about circles.

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

Make geometric constructions.

Reason with shapes and their attributes.

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

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

Apply geometric concepts in modeling situations.

Understand and apply the Pythagorean Theorem.

Apply trigonometry to general triangles.
problem_activity: Problem 1
The circumference of a circle is
$$32\pi$$
cm. What expression represents the exact area of the circle? If needed, draw a diagram to assist you.
Problem 2
Find the area and perimeter of the colored part of each figure below. The figures are composed of small squares with side length 1 unit and curves that are an arc of a circle.
a.
[IMG]
b.
[IMG]
Problem 3
A semi-circle with a diameter of 6 cm sits on top of an isosceles trapezoid. Find the area of the entire figure.
[IMG]


correct_option_index: 4