For the first one, I would write:
Now you can see this is 3 complete revolutions in the clockwise (negative) direction plus an additional negative amount...
Show the approximate location on the unit circle of for the given value of .
What's the 'process' behind showing where the points are?
I have tried adding/subtracting to obtain a point on the unit circle so I can have a general idea. It wasn't concrete.
You can use #1. as an example and I'll do the rest and post.
So, that is 4 clockwise revolutions from , which lands us back on , and from there we move counterclockwise to get on the unit circle which is the approximate location of
Does this mean ?
I was unsure because it led to: . It appears you factored.
How do you know where 2/3 lands?Originally Posted by MarkFL
It's a bit of an awkward number.
So, we are moving 7/8 of a revolution clockwise, which lands on .
The circle is divided into 4 parts, so in this case starting from (1,0) and counting clockwise, the third part is 75%. I then used this to approximate where 7/8 is the denominator is 4, so
Is always the starting point?
So go half way around in the negative direction, then continue a third of another half...
With due regards I have the following suggestion:
What so ever is the value of the angle write it in proper fraction e.g.,
23/4 π=(5+ 3/4 )π=4π+ π+ 3/4 π= π+ 3/4 π [ because even multiples ( positive or negative ) of π we reach OX the starting ray.
Now suppose it was negative we write it as sum of positive multiples of π and then subtract the angle. For example:
- 23/4 π=(-6+ 1/4 )π=-6π+ 1/4 π= 1/4 π [ because even multiples ( positive or negative ) of π we reach OX the starting ray.