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Bài 5 trang 41 SGK Toán 11 tập 1 - Chân trời sáng tạo

Tại các giá trị nào của x thì đồ thị hàm số y = cosx và y = sinx giao nhau?

🎀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

♓Tại các giá trị nào của x thì đồ thị hàm số y = cosx và y = sinx giao nhau?

Phương pháp giải - Xem chi tiết

Sử dụng công thức \(\sin x = cos\left( {\frac{\pi }{2} - x} \right)\) và giải phương trình côsin

Lời giải chi tiết

Đồ thị hàm số y = cosx và y = sinx giao nhau tại điểm x thoả mãn\(cosx = sinx \Leftrightarrow cosx = cos\left( {\frac{\pi }{2} - x} \right)\) \( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{2} - x + k2\pi \\x =  - \frac{\pi }{2} + x + k2\pi \end{array} \right. \Leftrightarrow x = \frac{\pi }{4} + k\pi ,k \in \mathbb{Z}.\)Vậy  \(x = \frac{\pi }{4} + k\pi ,k \in \mathbb{Z}.\)

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