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Giải bài 5 trang 9 sách bài tập toán 11 - Chân trời sáng tạo tập 1

Cho một góc lượng giác có số đo là \({375^0}\): a) Tìm số lớn nhất trong các số đo của góc lượng giác cùng tia đầu, tia cuối với góc đó mà có số đo âm;

꧃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

Cho một góc lượng giác có số đo là \({375^0}\): a) Tìm số lớn nhất trong các số đo của góc lượng giác cùng tia đầu, tia cuối với góc đó mà có số đo âm; b) Tìm số nhỏ nhất trong các số đo của góc lượng giác cùng tia đầu, tia cuối với góc đó mà có số đo dương. 

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về khái niệm góc lượng giác: Số đo của các góc lượng giác có cùng tia đầu Oa và tia cuối Ob sai khác nhau một bội nguyên của \({360^0}\) nên có công thức tổng quát là: \(\left( {Oa,Ob} \right) = {\alpha ^0} + k{360^0}\left( {k \in \mathbb{Z}} \right)\) với \({\alpha ^0}\) là số đo của một góc lượng giác bất kì có tia đầu Oa và tia cuối Ob.

Lời giải chi tiết

Góc lượng giác cùng tia đầu, tia cuối với góc có số đo là \({375^0}\) là: \({375^0} + k{360^0}\left( {k \in \mathbb{Z}} \right)\) a) Vì góc có số đo âm nên \({375^0} + k{360^0} < 0 \Leftrightarrow k < \frac{{ - 25}}{{24}}\). Mà k là số nguyên và góc có số đo âm lớn nhất nên \(k =  - 2\). Vậy góc cần tìm là: \({375^0} + \left( { - 2} \right){360^0} =  - {345^0}\) b) Vì góc có số đo dương nên \({375^0} + k{360^0} > 0 \Leftrightarrow k > \frac{{ - 25}}{{24}}\). Mà k là số nguyên và góc có số đo dương nhỏ nhất nên \(k =  - 1\). Vậy góc cần tìm là: \({375^0} + \left( { - 1} \right){360^0} = {15^0}\)

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