Question

What quadrant is 11pi/3 in? Find sin 0, cos 0, and tan 0. Find a positive and negative coterminal angle

Answer 1

@zepdrix Can you help me on this one?

Answer 2

Well we know the boundaries for each quadrant, right?
The first quadrant ends at pi/2
the second quadrant ends at pi
the third quadrant ends at 3pi/2

So let's compare our 11pi/3 to each of these values and see where it lies.

Get a common denominator between pi/2 and 11pi/3.
Which is larger?

Answer 3

no no no let's not do that :) my bad.

Answer 4

Haha okay!

Answer 5

11pi/3 is a really big angle, it's been spun around the entire circle a few times.
Let's first find our co-terminal angles.


We'll "unwind" it.
Let's subtract some 2pi's from it.

Answer 6

\[\large\rm \frac{11\pi}{3}-2\pi=?\]

Answer 7

9/3?

Answer 8

9pi/3?

Answer 9

No. Need to get a common denominator before you can perform subtraction.

Answer 10

5pi/3?

Answer 11

Ok great. So that's a `positive angle` which is co-terminal with 11pi/3.
How do we find a `negative angle` which is also co-terminal?
Any ideas? :)

Answer 12

Multiply by negative 1?

Answer 13

It's in the second quadrant right?

Answer 14

Multiply by -1.. Hmm, no. But that was a clever idea.
We'll "unwind" the angle even further.
We'll subtract another 2pi from it.

Q2? No.

Answer 15

Okay, -pi/3

Answer 16

What quadrant is it in?

Answer 17

Ok good :)
So that answers the third question they asked.

Answer 18

-pi/3 is probably the best angle to use to figure that out.
Where does -pi/3 put you?

Answer 19

Third?

Answer 20

Where is pi/3 located?

Answer 21

You gotta remember these three at the very least,
pi/6 pi/4 and pi/3

those are important :)

Answer 22

Okay, im not sure where though

Answer 23

So then if pi/3 puts us this far in the first quadrant

Answer 24

Then negative pi/3 is the same distance but spun in the opposite direction, ya?