Question

نقطه متناظر با زاویه -375 درجه در کدام ربع قرار دارد؟

پاسخ دانش آموز

ربع چهارم
ربع دوم
ربع اول
ربع سوم

Explanation:

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"concepts_used": [
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],
"new_concepts": [
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"Coterminal Angles",
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]
}
</pre_analysis>

<reasoning>

Find a positive coterminal angle

\[
\theta = -375^\circ + 2 \times 360^\circ = -375^\circ + 720^\circ = 345^\circ
\]

Determine the quadrant

\[
270^\circ < 345^\circ < 360^\circ \implies \text{Quadrant IV}
\]

Match with the options

\[
\text{Quadrant IV} \implies \text{ربع چهارم (Fourth Quadrant)}
\]
</reasoning>

<answer>
<mcq-correct>(A) ربع چهارم (Fourth Quadrant)</mcq-correct>
<mcq-option>(B) ربع دوم (Second Quadrant)</mcq-option>
<mcq-option>(C) ربع اول (First Quadrant)</mcq-option>
<mcq-option>(D) ربع سوم (Third Quadrant)</mcq-option>
</answer>

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<post_analysis>
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"Unit Circle Trigonometry"
]
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</post_analysis>

Answer:

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],
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"Unit Circle Trigonometry",
"Coterminal Angles",
"Quadrants of the Coordinate Plane"
]
}
</pre_analysis>

<reasoning>

Find a positive coterminal angle

\[
\theta = -375^\circ + 2 \times 360^\circ = -375^\circ + 720^\circ = 345^\circ
\]

Determine the quadrant

\[
270^\circ < 345^\circ < 360^\circ \implies \text{Quadrant IV}
\]

Match with the options

\[
\text{Quadrant IV} \implies \text{ربع چهارم (Fourth Quadrant)}
\]
</reasoning>

<answer>
<mcq-correct>(A) ربع چهارم (Fourth Quadrant)</mcq-correct>
<mcq-option>(B) ربع دوم (Second Quadrant)</mcq-option>
<mcq-option>(C) ربع اول (First Quadrant)</mcq-option>
<mcq-option>(D) ربع سوم (Third Quadrant)</mcq-option>
</answer>

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