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Giải bài 63 trang 31 sách bài tập toán 11 - Cánh diều

Cho lục giác đều \(ABCDEF\) nội tiếp trong đường tròn lượng giác (thứ tự đi từ \(A\) đến các đỉnh theo chiều dương).

🍎Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho lục giác đều \(ABCDEF\) nội tiếp trong đường tròn lượng giác (thứ tự đi từ \(A\) đến các đỉnh theo chiều dương). Khi đó, số đo của góc lượng giác \(\left( {OA,OC} \right)\) bằng: A. \(\frac{{2\pi }}{3} + k2\pi \)                                               B. \( - \frac{{2\pi }}{3} + k2\pi \) C. \(\frac{\pi }{3} + k2\pi \)                                          D. \( - \frac{\pi }{3} + k2\pi \)

Phương pháp giải - Xem chi tiết

Do lục giác đều \(ABCDEF\) nội tiếp trong đường tròn lượng giác tâm \(O\), nên ta có 6 góc bằng nhau: \(\widehat {AOB} = \widehat {BOC} = \widehat {COD} = \widehat {DOE} = \widehat {EOF} = \widehat {FOA} = {60^o} = \frac{\pi }{3}\) Sử dụng hệ thức Chasles để tính số đo của góc lượng giác \(\left( {OA,OC} \right)\)

Lời giải chi tiết

Vì lục giác đều \(ABCDEF\) nội tiếp đường tròn lượng giác tâm \(O\), nên ta có 6 góc bằng nhau: \(\widehat {AOB} = \widehat {BOC} = \widehat {COD} = \widehat {DOE} = \widehat {EOF} = \widehat {FOA} = {60^o} = \frac{\pi }{3}\)Do đó \(\widehat {AOC} = \frac{{2\pi }}{3} \Rightarrow \left( {OA,OC} \right) = \frac{{2\pi }}{3} + k2\pi \)Đáp án đúng là A.

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