tana = 3/4.
=>cota=1/ tana =1:3/4=4/3
sina /cosa =tana
=> sina =tana .cosa =3/4. cosa
lại có sin^2(a)+cos^2(a)=1
<=>9/16cos^2(a)+cos^2=1
<=>25/16cos^2(a)=1
<=>cos^2(a)=16/25
=>[cosa =4/5=>sina =3/5
    [cosa =-4/5=> sina =-2/5

Lời giải:

Do góc $a$ nhọn nên các tỉ số lượng giác mang giá trị dương.

Áp dụng công thức $\sin ^2a+\cos ^2a=1$

$\Rightarrow \cos^2 a=1-\sin ^2a=1-0,28^2=0,9216$

$\Rightarrow \cos a=\frac{24}{25}=0,96$

$\tan a=\frac{\sin a}{\cos a}=\frac{0,28}{0,96}=\frac{7}{24}$

$\cot a=\frac{1}{\tan a}=\frac{24}{7}$

\(\sin^2\widehat{A}+\cos^2\widehat{A}=1\Leftrightarrow\cos^2\widehat{A}=1-\dfrac{16}{25}=\dfrac{9}{25}\\ \Leftrightarrow\cos\widehat{A}=\dfrac{3}{5}\\ \tan\widehat{A}=\dfrac{\sin\widehat{A}}{\cos\widehat{A}}=\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{4}{3}\\ \cot\widehat{A}=\dfrac{1}{\tan\widehat{A}}=\dfrac{3}{4}\)

\(\sin A=0,8\Rightarrow A=arcsin0,8_{ }\)

\(\Rightarrow\cos A=cos\left(arcsin0,8\right)=\dfrac{3}{5}\)

     tanA=tan(arcsin0,8)=4/3

     cotA=1:4/3=3/4

\(\sin^2\widehat{A}+\cos^2\widehat{A}=1\Leftrightarrow\cos^2\widehat{A}=1-\left(\dfrac{3}{5}\right)^2=1-\dfrac{9}{25}=\dfrac{16}{25}\\ \Leftrightarrow\cos\widehat{A}=\dfrac{4}{5}\\ \tan\widehat{A}=\dfrac{\sin\widehat{A}}{\cos\widehat{A}}=\dfrac{3}{4}\\ \Rightarrow\cot\widehat{A}=\dfrac{1}{\tan\widehat{A}}=\dfrac{4}{3}\)