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Bài 7 trang 41 SGK Toán 11 tập 1 - Cánh diều

Số nghiệm của phương trình cosx = 0 trên đoạn \(\left[ {0;10\pi } \right]\) là

𒆙Tổng 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

Số nghiệm của phương trình cosx = 0 trên đoạn \(\left[ {0;10\pi } \right]\) là A.5 B.9 C.10 D.11

Phương pháp giải - Xem chi tiết

Sử dụng công thức tổng quát của phương trình cos

Lời giải chi tiết

Ta có\(\begin{array}{l}cosx{\rm{ }} = {\rm{ }}0\\ \Leftrightarrow cosx{\rm{ }} = {\rm{ cos}}\frac{\pi }{2}\\ \Leftrightarrow x{\rm{ }} = {\rm{ }}\frac{\pi }{2} + k\pi ;k \in Z\end{array}\)Mà \(x \in \left[ {0;10\pi } \right]\) nên \(\begin{array}{l}0 \le \frac{\pi }{2} + k\pi  \le 10\pi \\ \Rightarrow  - 0,5 \le k \le 9,5\end{array}\)Lại có \(k \in Z\) suy ra \(k \in \left\{ {0;1;2;3;4;5;6;7;8;9} \right\}\)Vậy phương trình đã cho có số nghiệm là 10.Chọn C

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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