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: Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Prove and apply trigonometric identities.

Interpret expressions for functions in terms of the situation they model.

Interpret functions that arise in applications in terms of the context.

Use functions to model relationships between quantities.

Analyze functions using different representations.
problem_activity: Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by
$${h(t)=-16t^2+79t+6}$$
where
$$h$$
is in feet and
$$t$$
is in seconds. The height of Andre's baseball is given by the graph below.
[IMG]
Brett claims that his baseball went higher than Andre’s, and Andre says that his baseball went higher.
Who is right?
How long is each baseball airborne?
Construct a graph of the height of Brett’s throw as a function of time on the same set of axes as the graph of Andre’s throw, and explain how this can confirm your claims to parts (a) and (b).


correct_option_index: 0

3

9

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