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Giải câu hỏi trắc nghiệm trang 72 vở thực hành Toán 9

Cho tam giác ABC có (widehat A = {90^o}) (H 4.2). A. (sin B = frac{{AB}}{{BC}}). B. (cos C = frac{{AC}}{{AB}}). C. (tan B = frac{{AC}}{{AB}}). D. (cot C = frac{{AB}}{{BC}}).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Chọn phương án đúng trong mỗi câu sau:

Câu 1

Trả lời Câu 1 trang 72 Vở thực hành Toán 9

Cho tam giác ABC có \(\widehat A = {90^o}\) (H 4.2).

 

A. \(\sin B = \frac{{AB}}{{BC}}\). B. \(\cos C = \frac{{AC}}{{AB}}\). C. \(\tan B = \frac{{AC}}{{AB}}\). D. \(\cot C = \frac{{AB}}{{BC}}\).

Phương pháp giải:

Xét tam giác ABC vuông tại A có góc nhọn B bằng \(\alpha \). Ta có: + Tỉ số giữa cạnh đối và cạnh huyền gọi là sin của \(\alpha \). + Tỉ số giữa cạnh kề và cạnh huyền gọi là cos của \(\alpha \). + Tỉ số giữa cạnh đối và cạnh kề gọi là tan của \(\alpha \). + Tỉ số giữa cạnh kề và cạnh đối gọi là cot của \(\alpha \).

Lời giải chi tiết:

Vì tam giác ABC có \(\widehat A = {90^o}\) nên \(\tan B = \frac{{AC}}{{AB}}\) Chọn C

Câu 2

Trả lời Câu 2 trang 72 Vở thực hành Toán 9

Cho tam giác ABC có \(\widehat A = {90^o}\)  và \(\widehat C = {30^o}\) như trên Hình 4.3. Tìm khẳng định sai trong các khẳng định sau?

 

A. \(\sin B = \frac{{\sqrt 3 }}{2}\). B. \(\cos C = \frac{{\sqrt 3 }}{2}\). C. \(\tan B = \sqrt 3 \). D. \(\cot B = \frac{1}{2}\).

Phương pháp giải:

+ Tính góc B. + Sử dụng bảng giá trị lượng giác của các góc 30 độ và 60 để tính.

Lời giải chi tiết:

Vì tam giác ABC có \(\widehat A = {90^o}\) nên \(\widehat B = {90^o} - \widehat C = {60^o}\). Suy ra \(\sin B = \cos C = \sin {60^o} = \frac{{\sqrt 3 }}{2};\tan B = \tan {60^o} = \sqrt 3 ;\cot B = \cot {60^o} = \frac{{\sqrt 3 }}{3}\). Chọn D

Câu 3

Trả lời Câu 3 trang 72 Vở thực hành Toán 9

Cho \(\alpha \), \(\beta \) là hai góc nhọn trong tam giác ABC (H.4.4). Khi đó

 

A. \(\sin \alpha  = \tan \beta \). B. \(\cos \alpha  = \cot \beta \). C. \(\tan \alpha  =  - \cot \beta \). D. \(\cot \alpha  = \tan \beta \).

Phương pháp giải:

Nếu hai góc phụ nhau thì sin góc này bằng côsin góc kia, tang góc này bằng côtang góc kia.

Lời giải chi tiết:

Vì tam giác ABC vuông tại C nên \(\widehat A + \widehat B = {90^o}\), suy ra \(\alpha  + \beta  = {90^o}\). Do đó, \(\cot \alpha  = \tan \beta \). Chọn D

Câu 4

Trả lời Câu 4 trang 72 Vở thực hành Toán 9

A. \(\sin {82^o} =  - \cos {8^o}\). B. \(\cos {75^o} = \sin {16^o}\). C. \(\cot {52^o} =  - \tan {28^o}\). D. \(\tan {30^o}40' = \cot {59^o}20'\).

Phương pháp giải:

Nếu hai góc phụ nhau thì sin góc này bằng côsin góc kia, tang góc này bằng côtang góc kia.

Lời giải chi tiết:

Vì \({30^o}40' + {59^o}20' = {90^o}\) nên \(\tan {30^o}40' = \cot {59^o}20'\) Chọn D

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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