Which direction will you face if you start facing
(a) east and make $\frac{1}{2}$ of a revolution clockwise?
(b) east and make $1\frac{1}{2}$ of a revolution clockwise?
(c) west and make $\frac{3}{4}$ of a revolution anti-clockwise?
(d) south and make one full revolution?
(should we specify clockwise or anti-clockwise for this last question? Why not?)

To do :

We have to find the direction we face in each case.

Solution :

We know that,

1 revolution $= 360^o$

Therefore,

(a) $\frac{1}{2}$ revolution $= \frac{360^o}{2} = 180^o$

The direction, $180^o$ from the east is the west.

Therefore, if we start facing east and make $\frac{1}{2}$ of a revolution in the clockwise direction, then we will face the west direction.

 (b) $1\frac{1}{2}$ revolution $= \frac{3}{2}\times 360^o = 540^o$

We complete a full revolution and then complete half a revolution from the same starting point.

This implies,

The direction, $180^o$ from the east is the west.

Therefore, if we start facing east and make $1\frac{1}{2}$ of a revolution in the clockwise direction, then we will face the west direction.

(c) $\frac{3}{4}$ revolution $= \frac{3}{4}\times360^o = 270^o$

From west we make $\frac{3}{4}$ of a revolution anti-clockwise.

This implies,

The direction, $270^o$ from the west is the North.

Therefore, if we start facing west and make $\frac{3}{4}$ of a revolution in the anti-clockwise direction, then we will face the north direction.

(d) If we start facing South and make one full revolution, then we will face the same starting South direction.

In case of revolving 1 complete revolution, either clockwise or anti-clockwise we will be back at the starting position.