Question

if the given angle makes complete five rotations in anticlockwise sense then what will be the measure of that angle ​

Answer 1

Answer:

Why do we measure the angle anticlockwise?

We had to pick one option!

In mathematics, it kinda makes sense that angles are (by convention) measured relative to the positive X axis and that positive angles take you up into the positive Y direction. This results in an anticlockwise system of angles.

In mapping and navigation, compass directions were chosen in the clockwise direction…and it could be argued that this comes from the way sundials and compasses work.

A compass points “North” - and a sundial has to be oriented to face North. When you do that (in the Northern hemisphere, where such devices were first used) - the shadow on the sundial moves clockwise - and it kinda makes sense that we measure angles in the same direction as the clock. But you could certainly make an argument that the direction that clock hands move is because of the way compasses were first used - and not the other way around!

This is evident not just in the clockwise/anticlockwise difference - but also that geographical “heading” is measured relative to North - where in math it’s measured relative to +X - which is “East”.

My present job is in flight simulation - where we get inputs in mapping/navigation angles and have to use math and computer graphics which use the mathematical convention.

You wouldn’t believe the amount of grief this causes…and don’t even let me get started on how people say “Latitude, Longitude, Altitude” but also “X, Y, Z” - resulting in the first map coordinate being the vertical one and the first mathematical coordinate being the horizontal one - or how aeronautical altitudes are still stated in feet - even though everything else is in meters.