Additional Mathematics – Trigonometry | e-Consult

1. Apply \(\sin^{2}A+\cos^{2}A=1\):

   \[

   \left(\frac{3}{5}\right)^{2}+\cos^{2}A=1\;\Longrightarrow\;\frac{9}{25}+\cos^{2}A=1

   \]

   \[

   \cos^{2}A=1-\frac{9}{25}=\frac{16}{25}

   \]

2. Since \(A\) is acute, \(\cos A>0\):

   \[

   \cos A=\frac{4}{5}

   \]

3. Find \(\tan A\) using \(\tan A=\dfrac{\sin A}{\cos A}\):

   \[

   \tan A=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}

   \]

Therefore \(\displaystyle \cos A=\frac{4}{5}\) and \(\displaystyle \tan A=\frac{3}{4}\).