Point P(t) on unit circle

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.

Re: Point P(t) on unit circle

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...

Re: Point P(t) on unit circle

Quote:

Originally Posted by

**MarkFL** 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...

But how do you know where to start, in order to go the 3 revolutions?

You can't start at or .

Re: Point P(t) on unit circle

You start at which is the point (1,0)...

Re: Point P(t) on unit circle

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.

Re: Point P(t) on unit circle

Quote:

Originally Posted by

**Unreal**

No, this is incorrect... is less than one complete revolution, so you simply move radians in the negative (clockwise) direction. Since:

, we know we need to make 2/3 of a complete revolution.

Quote:

Originally Posted by

**Unreal** ASIDE:

Does this mean

?

I was unsure because it led to:

. It appears you factored.

Yes, both are the same... .

Re: Point P(t) on unit circle

Quote:

Originally Posted by **MarkFL**

Since:

, we know we need to make 2/3 of a complete revolution.

How do you know where 2/3 lands?

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?

Re: Point P(t) on unit circle

Quote:

Originally Posted by

**Unreal** How do you know where 2/3 lands?

It's a bit of an awkward number.

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...

Quote:

Originally Posted by

**Unreal**
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

You can always add an integral multiple of to get to the same place...:

Quote:

Originally Posted by

**Unreal** Is

always the starting point?

Yes, that's where we begin when we measure an angle on the unit circle.

Re: Point P(t) on 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.