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Bài 1.23 trang 40 SGK Toán 11 tập 1 - Kết nối tri thức

Biểu diễn các góc lượng giác

꧙Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

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

Biểu diễn các góc lượng giác \(\alpha  =  - \frac{{5\pi }}{6},\;\beta  = \frac{\pi }{3},\;\gamma  = \frac{{25\pi }}{3},\delta  = \frac{{17\pi }}{3}\) trên đường tròn lượng giác. Các góc nào có điểm biểu diễn trùng nhau?       A. \(\beta \) và \( \gamma \)                           B. \(\alpha, \beta, \gamma \)                                  C. \(\beta ,\gamma ,\delta \)                            D. \(\alpha \) và \(\beta \),

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Để biểu diễn cung lượng giác trên đường tròn lượng giác, ta áp dụng: - Cung có số đo \(\alpha \;\left( {{\alpha ^0}} \right)\) và cung có số đo \(\alpha  + k2\pi \;\left( {{\alpha ^0} + k{{360}^0}} \right)\) có cùng điểm biểu diễn trên đường tròn lượng giác

Lời giải chi tiết

Ta có: \(\frac{{25\pi }}{3} = \frac{\pi }{3} + 4.2\pi .\) Do đó điểm biểu diễn cung lượng giác \(\frac{{25\pi }}{3}\) trùng với điểm biểu diễn cung lượng giác \(\frac{\pi }{3}\).Vậy ta chọn đáp án A

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