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...
Hi!
Show the approximate location on the unit circle of for the given value of .
1.
2.
3.
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
ASIDE:
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?
It may be easier to just think of it in its original form...
So go half way around in the negative direction, then continue a third of another half...
You can always add an integral multiple of to get to the same place...:
Yes, that's where we begin when we measure an angle on the unit circle.
With due regards I have the following suggestion:
Whatsoever is
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.