Question

medal award!

Answer 1

Make sure you remember how to read these brackets.
Square bracket means we include the point,
round bracket is exclusion.\[\large\rm t\in[0,2\pi)\qquad\to\qquad 0\le t\lt 2\pi\]

Answer 2

t=2pi isn't in our interval, ya?

Answer 3

it is totally in our interval :D

Answer 4

Nooo :O

Answer 5

Round bracket on the 2pi

Answer 6

Darn! I keep forgetting. It would be like this (2pi)

Answer 7

\[\huge\rm t\in[0,2\pi\color{red}{)}\qquad\to\qquad 0\le t\color{red}{\lt} 2\pi\]No 2pi allowed :OOO

Answer 8

so whenever they are asking the distance what exactly do they want?

Answer 9

Well... you're right.
If we spun 2pi, we'd get to the point they labeled.

So we need a value that is `co-terminal with 2pi` and inside our interval.

Answer 10

If we spin around 2pi, we get to 4pi.
That's way way outside of our interval though.

Can we go backwards and get to a value in our interval maybe?

Answer 11

Don't know if this is right but maybe pi/2?

Answer 12

No.
You need to spin a full rotation to find co-terminal angles.
full rotation = 2pi, ya?

Answer 13

So if we're at 2pi, and we spin backwards an entire rotation,
where do we land?

Answer 14

-2pi?

Answer 15

Hmm that certainly is co-terminal with 2pi :)

But from 2pi, you spun around the circle TWICE to get to -2pi.
Too far. That's outside of our interval.

Answer 16

You're gonna be so mad when you figure out how simple this was LOL

Answer 17

pi/6?

Answer 18

pi/6 is not co-terminal to 2pi :c

Should I just spill the beans? :3

Answer 19

yes :D I honestly don't know what it is

Answer 20

We're starting at (1,0) and ending at (1,0).
In order for this to happen, we have to spin multiples of 2pi.

If we're between 0 and 2pi (excluding the value 2pi),
then we have to spin how many 2pi's around to land in the same spot?
0 of them.

t=0

Answer 21

o wow. XD

Answer 22

it's really that simple :)

Answer 23

Ya, kind of a trick question :c

The point to point tells us that we have to move 2pi's.
But the interval tells us that we're not able to.
So you can't move at all :p

Answer 24

thank you zepdrix :)