i need help with terminal points .

Question

i need help with terminal points >.<
please help.
i'll post the picture in a bit.

anonymous · Answer

attachment

anonymous · Answer

number 33

e.mccormick · Answer

OK, you have some angle t and it has a terminal point as given there.  If you use the terminal point, you can find the angle. OR you can use a little logic here.

e.mccormick · Answer

$\pi$ is half way around the unit circle. $2\pi$ is all the way around.  With just those facts, what can you say about any of the equations?  Start with d.  It is the easy one.

anonymous · Answer

2pie-t=
do i just substitute (3,5) or (4,5)??

e.mccormick · Answer

The numbers in the point are fractions.  They stay fractions.

anonymous · Answer

(3/5) or (4/5)

e.mccormick · Answer

This should help. A 1 unit circle, and the point $\left(\frac{3}{5},\frac{4}{5}\right)$ on it. https://www.desmos.com/calculator/2kgjonrf8n

anonymous · Answer

im still confuse >.<

e.mccormick · Answer

You see the point and the circle, right?  That is what they are taling about so lets start there.

anonymous · Answer

okay

e.mccormick · Answer

So there is some angle that goes along and makes that point the terminal.  We don't know what it is, and we do not really care.  What we want to know is where would the terminal point land if we added or subtracted things involving this angle.  But not just anything.  We want the known angles, $pi$ and $2pi$.

anonymous · Answer

ohh okay

e.mccormick · Answer

So if I draw in the angle's line, I get this: https://www.desmos.com/calculator/qa0oenlykq

e.mccormick · Answer

Now... this is why I said d is the best one to start with.  If I add $2\pi$ to that angle, no matter what that angle is, where does the angle land?

anonymous · Answer

quadrant 1?

e.mccormick · Answer

Well, I meant a little more specific.  Yes, in this case it is from Q1 back to Q1.  But lets look a little closer.

Heard the term coterminal angle used recently?

anonymous · Answer

no

e.mccormick · Answer

Ah.  OK.  If I start at 0 and I add $2\pi$ I end up back at 0!  This is the first coterminal angle people get to see.  Because $2\pi$ is a full revolution, the terminal point is the same!

e.mccormick · Answer

Now, apply that principal to part d.  What does that mean the terminal point is after you add $2\pi$ to t?

anonymous · Answer

that it'll be at the same place , 0?

e.mccormick · Answer

For 0 the same place is 0.  For some random angle that ends on $\left(\frac{3}{5},\frac{4}{5}\right)$ it is?

anonymous · Answer

((3/5),(4/5))

e.mccormick · Answer

Exactly.  Doing a drawing here cause it is easier to edit than desmos.

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