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

View Explanation

Log in for full answers

Similar Questions

Which of the following related acute angle expressions is equivalent to ?

Given the angle measure A, B, C, D, cos ⁡ ( 𝜃 ) appears equal to the cosine of which angle measure?

MTH1010_09_01_1

MTH1010_09_02_3

MTH1010_09_01_4

MTH1010_09_01_1

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler