Question

What part of a revolution have you turned through if you stand to face:
(a) East and turn clockwise to face north?
(b) South and turn clockwise to face east?
(c) West and turn clockwise to face east?

Answer 1

The degrees of rotation in the unit circle are regularly connected with the directional designations, which is required for navigational calculations (derived from trigonometry) and usage with Global Positioning Satellite (GPS) receivers. The four intermediate compass directions placed halfway between each pair of cardinal directions are known as intercardinal (intermediate, or historically, ordinal).

Complete Step By Step Answer:
The four cardinal directions, sometimes known as cardinal points, are north, east, south, and west, and are typically indicated by the letters N, E, S, and W. East and west are perpendicular to north and south (at right angles), with east rotating clockwise from north and west rotating exactly opposite east. The compass points are the intersections of the cardinal directions. Northeast (NE), southeast (SE), southwest (SW), and northwest (NW) are the ordinal (also known as intercardinal) directions (NW). The eight shortest points in the compass rose displayed to the right are called secondary intercardinal directions, which are the intermediate direction of every combination of intercardinal and cardinal directions (e.g. NNE, ENE, and ESE).
(a)There is one right angle from east to south, one right angle from south to west, and one right angle from west to north here.
As a result, the east-to-north turn is three right angles. To turn from east to north, it takes $\dfrac{3}{4}$ of a revolution.
(b) There are three right angles in the turn from south to east. i.e. one right angle from south to west, one right angle from west to north, and one right angle from north to east. To turn from south to east, it takes $\dfrac{3}{4}$ of a revolution.
(c) The west-to-east twists, resulting in two right angles. From west to east, half a rotation is necessary.

Note:
Cartographers make conventional maps with north (N) at the top and east (E) at the right, with the cardinal points correctly delineated. Cardinal directions provide the cornerstone of a framework for informing someone how to reach those locations, and maps give a systematic way to record where places are. North does not have to be at the very top of the list. In mediaeval Europe, for example, most maps out east (E) at the top. South-up maps are preferred by a few cartographers.