MTH1010_09_10_2

Question

MTH1010_09_10_2

BlackTom AI · Accepted Answer

The provided data shows a mismatched set of inputs:
- The JSON has question_type as a short_answer_question with answer: ["6"], but no answer_options are supplied.
- The accompanying image (not strictly part of the JSON) displays a classic trigonometry multiple-choice problem about cos(θ) = 3/5 and sin(θ) = 4/5, with four angle-range options (a) through (d).
Because the options are missing in the JSON, we cannot analyze options that aren’t given. Instead, I’ll reason about the typical intention of the trig problem suggested by the image and how the numeric answer might be interpreted.

Typical interpretation (based on cos(θ)=3/5 and sin(θ)=4/5):
- If cos(θ) = 3/5 and sin(θ) = 4/5, then both cosine and sine are positive, so θ lies in the first quadrant.
- The angle in the first quadrant with these exact sine and cosine values corresponds to a specific angle θ such that tan(θ) = sin(θ)/cos(θ) = (4/5)/(3/5) = 4/3, and θ = arctan(4/3).
- The general solution would be θ = arctan(4/3) + 2πk, where k is any integer.
- If the problem asks for the number of solutions in a standard interval (for example 0 ≤ θ < 2π), there is exactly one such θ in that interval, namely θ = arctan(4/3) in QI.

Why the answer 6 might be inconsistent:
- The value 6 does not correspond to a standard count of solutions for this type of problem within a typical fundamental interval (0 to 2π) unless the question asked for something else (e.g., a total count over a much larger interval or a different equation). Without the explicit question prompt and answer choices, we cannot validate that 6 is correct.

In summary:
- Given cos(θ)=3/5 and sin(θ)=4/5, there is a single θ in 0 ≤ θ < 2π (namely in QI) that satisfies both, and the general solution is θ = arctan(4/3) + 2πk.
- The provided JSON lacks answer options to analyze, so a definitive justification for why “6” is correct cannot be given from the current data. If you can supply the exact question prompt (in-text) or the full list of answer choices, I can tailor the reasoning precisely to that format.

MCD2130 - T2 - 2025 10.7 Online Quiz - MCD2130_QUIZ_NINE Circular Functions, Continuity and Differentiability

MTH1010_09_10_2

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