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Bài 7 trang 20 SGK Toán 11 tập 1 - Chân trời ság tạo

Thanh OM quay ngược chiều kim đồng hồ quanh trục O của nó trên một mặt phẳng thẳng đứng và in bóng vuông góc xuống mặt đất như Hình 12. Vị trí ban đầu của thanh là OA. Hỏi độ dài bóng O’M’ của OM khi thanh quay được (3frac{1}{{10}}) vòng là bao nhiêu, biết thanh độ dài OM là 15cm? Kết quả làm trong đến hàng phần mười.

💛Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

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

🌃Thanh OM quay ngược chiều kim đồng hồ quanh trục O của nó trên một mặt phẳng thẳng đứng và in bóng vuông góc xuống mặt đất như Hình 12. Vị trí ban đầu của thanh là OA. Hỏi độ dài bóng O’M’ của OM khi thanh quay được \(3\frac{1}{{10}}\) vòng là bao nhiêu, biết thanh độ dài OM là 15cm? Kết quả làm trong đến hàng phần mười.

 

Phương pháp giải - Xem chi tiết

Dựa vào hàm lượng giác cơ bản để tính.

Lời giải chi tiết

Đặt hệ trục tọa độ như hình:

Thanh OM quay được \(3\frac{1}{{10}}\) \( \Rightarrow \alpha  = 3\frac{1}{{10}}.360^\circ  = 1116^\circ \). Kẻ MH vuông góc Ox, H thuộc Ox. Khi đó \(\begin{array}{l}M\left( {15.\cos 1116^\circ ;15.\sin 1116^\circ } \right)\\ \Rightarrow OH = \left| {\cos 1116^\circ } \right|.15 \approx 12,1\end{array}\). Vậy độ dài bóng O’M’ của OM khi thanh quay được \(3\frac{1}{{10}}\) là 12,1cm.

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