Question

What is an expression for all possible angles coterminal with 30 degrees in general form?

Answer 1

30+360n, where n is an integer.

Answer 2

How did you figure that out? =)

Answer 3

Coterminal angles are angles that land in the same "spot" on the unit circle.

Answer 4

So, when you go one full rotation (to get back to the same spot), you travel 360 degrees either clockwise or counterclockwise.

Answer 5

And you can spin as many times as you want.

Answer 6

That is why n can be any integer.

Answer 7

Does that explanation help at all?

Answer 8

Yes. Thank you. =)

Answer 9

No worries

Answer 10

How about for 3 pi / 2?

Answer 11

Same concept applies, but for radians 1 rotation is 2π. Any ideas, guesses?

Answer 12

2 pi n + 3 pi/2?

Answer 13

Right, where n is an integer. Good job!

Answer 14

Awesome!

Answer 15

:)

Answer 16

Can I please ask you another question?

Answer 17

Sure.

Answer 18

For each angle in standard position, determine one positive and negative angle that is coterminal with it. pi/3

Answer 19

If you can write a formula for any cotermial angle, then you would just need to plug in two integers for n to find 2 coterminal angles, one positive and one negative.

Answer 20

also, the question with the 30 degree angle, does the expression lie in the domain\[-720 degrees \le \theta < 1080 \]?

Answer 21

That depends on what you choose for n.

Answer 22

but is that expression applicable here in general?

Answer 23

Not unless you restrict your n to only give you values in that domain.

Answer 24

then what can n be restricted to?

Answer 25

Whatever you need it to be. When n is 0, θ is 30, so that is in your domain. When n is -1, θ is -330, so that is good too.

Answer 26

When n is -2, θ is -690. Is that in the domain?

Answer 27

It should be.

Answer 28

For the other question and the coterminal angles.... pi/3, is there an easier way to solve it without plugging it in the formula?

Answer 29

Right. Could n be -3 and θ be in the domain?

Answer 30

Not that I know of off hand...

Answer 31

yes, it can because theta can be greater than 720 degrees and my answer is -1,050

Answer 32

I thought it couldn 't be less than -720.

Answer 33

\[-720 \le \theta < 1080\]

Answer 34

You don 't have to plug in every value though. You can skip if it seems you have enough room.

Answer 35

It looks good though.

Answer 36

For the other question and the coterminal angles.... pi/3, is there an easier way to solve it without plugging it in the formula?

Answer 37

You don 't have to plug in every value for n. You can skip if it seems you have enough room.