Question

If $\sin A=\frac{3}{4}$, calculate $\cos A$ and $\tan A$

• A. $\cos A=\frac{\sqrt{3}}{4}$ and $\tan A=\frac{2}{5}$
• B. $\cos A=\frac{\sqrt{7}}{4}$ and $\tan A=\frac{3}{\sqrt{7}}$
• C. Both A and B
• D. None of these

Answer 1

Answer: (B)

$\cos A=\frac{\sqrt{7}}{4}$ and $\tan A=\frac{3}{\sqrt{7}}$

Given,

$\sin A=\frac{3}{4}$......(1).

or, $\cos A=\sqrt{1-{\sin }^{2}A}$

or, $\cos A=\sqrt{1-{\left(\frac{3}{4}\right)}^2}$

or, $\cos A=\frac{\sqrt{7}}{4}$......(2).

From (1) and (2) we have,

$\tan A=\frac{3}{\sqrt{7}}$.