ta có:

 . \(\hept{\begin{cases}tan\alpha=\frac{sin\alpha}{cos\alpha}\\cot\alpha=\frac{cos\alpha}{sin\alpha}\\tan\alpha\times cot\alpha=1\end{cases}}\)

Áp dụng định lý Pitago:

\(AB=\sqrt{BC^2+AC^2}=15\left(cm\right)\)

\(sinA=\dfrac{BC}{AB}=\dfrac{12}{15}=\dfrac{4}{5}\)

\(cosB=\dfrac{BC}{AB}=\dfrac{4}{5}\)

\(tanA=\dfrac{BC}{AC}=\dfrac{12}{9}=\dfrac{4}{3}\)

\(cotB=\dfrac{BC}{AC}=\dfrac{4}{3}\)

Áp dụng định lí Pytago vào ΔABC vuông tại C, ta được:

\(AB^2=CA^2+CB^2\)

\(\Leftrightarrow AB^2=9^2+12^2=225\)

hay AB=15(cm)

Xét ΔABC vuông tại C có 

\(\sin\widehat{A}=\dfrac{CB}{AB}=\dfrac{12}{15}=\dfrac{4}{5}\)

\(\cos\widehat{B}=\dfrac{CB}{AB}=\dfrac{12}{15}=\dfrac{4}{5}\)

\(\tan\widehat{A}=\dfrac{CB}{CA}=\dfrac{12}{9}=\dfrac{4}{3}\)

\(\cot\widehat{B}=\dfrac{CB}{CA}=\dfrac{12}{9}=\dfrac{4}{3}\)

\(\cot\widehat{C}=\dfrac{5}{12}\)

\(\sin\widehat{C}=\dfrac{12}{13}\)

\(\cos\widehat{C}=\dfrac{5}{13}\)

Bài 1:

Áp dụng định lí pytago trong tam giác vuông ABC ta có:

BC²=AC²+AB²

BC²=4²+3²

BC=\(\sqrt{25}\)=5(cm)

Ta có:

Sin B=\(\dfrac{AC}{BC}=\dfrac{4}{5}=0.8\)

Cos B=\(\dfrac{AB}{BC}=\dfrac{3}{5}=0.6\)

Tag B=\(\dfrac{AC}{AB}=\dfrac{4}{3}\)

Cotg B=\(\dfrac{AB}{AC}=\dfrac{3}{4}=0.75\)

bài 2:

\(\sin\alpha^2+\cos\alpha^2=1\)

=>0,6²+\(\cos\alpha^2=1\)

=>\(\cos\alpha=0,8\)

\(\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=>\tan\alpha=\dfrac{0,6}{0,8}=0,75\)

\(\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}=\dfrac{0,8}{0,6}\)\(\approx1,33\)

\(\cos\widehat{B}=\sqrt{1-0.28^2}=\dfrac{24}{25}\)

\(\tan\widehat{B}=\dfrac{7}{24}\)

\(\cot\widehat{B}=\dfrac{24}{7}\)