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Giải hoạt động mở đầu trang 35 SGK Toán 11 tập 1 - Chân trời sáng tạo

Trong hình bên, khi bàn đạp xe đạp quay, bóng M của đầu trục quay dao động trên mặt đất quanh điểm O theo phương trình

𝔍Tổng 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

Trong hình bên, khi bàn đạp xe đạp quay, bóng M của đầu trục quay dao động trên mặt đất quanh điểm O theo phương trình \(s = 17cos5\pi t\;\)với s (cm) là toạ độ của điểm M trên trục Ox là t (giây) là thời gian bàn đạp quay. Làm cách nào để xác định được các thời điểm mà tại đó độ dài bóng OM bằng 10cm?

Phương pháp giải - Xem chi tiết

Dựa vào hình ảnh và phương trình s.

Lời giải chi tiết

Độ dài bóng OM bằng 10 cm khi s = 10 hoặc s = -10.Khi s = 10. Ta có: \(17cos5\pi t = 10 \Leftrightarrow cos5\pi t = \frac{{10}}{{17}}\)Khi s = 10. Ta có: \(17cos5\pi t =  - 10 \Leftrightarrow cos5\pi t = \frac{{ - 10}}{{17}}\)Từ đó, ta có thể xác định được các thời điểm t bằng cách giải phương trình côsin.

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

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