few_shots: 
Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

HS_0
standard_description: Solve quadratic equations with real coefficients that have complex solutions.
problem_activity: Task
The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the values that are given but some of their output values are missing.
{"table": [{"tbody": [{"tr": [{"th": [{"_value": "$t$"}], "td": [{"_value": "0"}, {"_value": "15"}, {"_value": "30"}, {"_value": "45"}, {"_value": "60"}, {"_value": "75"}, {"_value": "90"}, {"_value": "105"}, {"_value": "120"}]}, {"th": [{"_value": "$f(t)$"}], "td": [{"_value": "0"}, {"_value": "0.5"}, {}, {"_value": "1.3"}, {"_value": "2"}, {"_value": "2.7"}, {}, {"_value": "4"}, {}]}, {"th": [{"_value": "$g(t)$"}], "td": [{"_value": "0"}, {"_value": "0.5"}, {}, {"_value": "1.3"}, {"_value": "2"}, {"_value": "2.7"}, {}, {"_value": "4"}, {}]}]}]}]}
Complete the table in a way so that $f$ could be invertible and so that $g$ is definitely not invertible.
Graph both functions and explain from the graph why $f$ is invertible and $g$ is not.
Come up with two real life situations that $f$ and $g$ could be representing.
Find and interpret the value $f^{-1}(4)$ in terms of these contexts.


aligns: no