Question

A line $l$ passing through the origin makes and angle $\theta$ with positive direction of x-axis such that $\sin \theta =\frac{3}{5}$. The coordinates of the point, which lies in the fourth quadrant at a unit distance from the origin and on perpendicular to $l$, are

• A. $(\frac{3}{5},-\frac{4}{5})$
• B. $(\frac{4}{5},-\frac{3}{5})$
• C. $(3,-4)$
• D. $(4,-3)$

Answer 1

The correct option is A $(\frac{3}{5},-\frac{4}{5})$

$\sin (90-\theta )=\frac{BE}{1};\cos \theta =\frac{BE}{1}=\frac{4}{5}$
$BE=\frac{4}{5}$
$AB=\sqrt{1-{\left(\frac{4}{5}\right)}^2}=\frac{3}{5}\therefore E(\frac{3}{5},-\frac{4}{5})$