The equation of the hour hand at 4 o'clock is | vedclass

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Question

(C) The hour hand,minute hand,and second hand of a clock always pass through the origin $(0,0)$ because one end of these hands is fixed at the center

Vedclass · Accepted Answer

$x + \sqrt{3}y = 0$

Vedclass · Answer

(C) The hour hand,minute hand,and second hand of a clock always pass through the origin $(0,0)$ because one end of these hands is fixed at the center of the clock.At $4$ o'clock,the hour hand makes an angle of $30^{\circ}$ with the positive $x$-axis in the fourth quadrant (as shown in the figure).The angle made by the line with the positive $x$-axis is $	heta = -30^{\circ}$.The slope of the line is $m = 	an(-30^{\circ}) = -\frac{1}{\sqrt{3}}$.The equation of a line passing through the origin with slope $m$ is $y = mx$.Substituting the value of $m$,we get $y = -\frac{1}{\sqrt{3}}x$.Multiplying both sides by $\sqrt{3}$,we get $\sqrt{3}y = -x$,which simplifies to $x + \sqrt{3}y = 0$.

The equation of the hour hand at $4$ o'clock is

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