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: Understand ratio concepts and use ratio reasoning to solve problems.

Analyze proportional relationships and use them to solve real-world and mathematical problems.
problem_activity: Hummingbird feeders can be filled with a simple sugar water mixture. Two different recipes are shown below.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"div": [{"_attributes": {"class": ["table-responsive"]}, "table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width: 80%;"}, "caption": [{"_value": "Recipe 1"}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Water (cups)"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Sugar (cups)"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$16$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$28$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$7$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$32$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$8$$"}]}]}]}]}]}]}, {"div": [{"_attributes": {"class": ["table-responsive"]}, "table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width: 80%;"}, "caption": [{"_value": "Recipe 2"}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Water (cups)"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Sugar (cups)"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2\\frac{2}{3}$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1\\frac{1}{2}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$8$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$3$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$24$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$9$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$32$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$12$$"}]}]}]}]}]}]}]}]}]}]}
Compare the two different recipes. Which recipe is more sugary? Justify your response.


correct_option_index: 0