Question

Cos and sin with Unit Circle

Answer 1

Here are the problems:

2: a) cos (-3pi/2) b) sin (-3pi/2)
My Answer: a) 0 b) -1
4: a) cos (15pi/4) b) sin (15pi/4)
My Answer: a) sqrt(2)/2 b) -sqrt(2)/2
6: a) cos (4pi/3) b) sin (4pi/3)
MA: a) -1/2 b) -sqrt(3)/2
8: a) cos(300 DEGREES) b) sin (300 degrees)
MA: a) sqrt(3)/2 b) -1/2
10: cos (-360030 degrees) b) sin (360030 degrees)
MA: -sqrt(2)/2 b) sqrt(2)/2

Answer 2

@FortyTheRapper

Answer 3

4 and 6 and 10 look good, I would recheck 2 and 8

Answer 4

Okay, I'll do that now

Answer 5

Wait 2 is right

Answer 6

So I should redo 8?

Answer 7

Right, your signs are right. It's just the values

Answer 8

Okay...one minute

Answer 9

I think I went wrong somewhere still
300 - 180 takes me to pi, then another 90 takes me to 270 degrees, another 30 degrees takes me to pi/6 ( in fourth quadrant) which is sqrt3/2, -1/2. Where did I mess up?

Answer 10

The first and third quadrants start with pi/6
The second and fourth quadrants start with pi/3

It's kinda like reflecting one side of the circle across the x (or y) axis

Answer 11

Oh. So it takes me to pi/3 which is (1/2, - sqrt(3)/2)?

Answer 12

Correct

Answer 13

Hmm, okay. I'll have to remember the reflection part.
Can you help me with #9?
cos (360045 degrees) b) sin (360045 degrees)
I got cos right, but not sin

Answer 14

What were your answers?

Answer 15

a) sqrt(2)/2 b) -sqrt(2)@

Answer 16

So

360,045

Would you agree 360 can go into 360,000 evenly?

Answer 17

Yes,

Answer 18

Alright, so lets subtract that out

\[360,045-360,000 = 45\]

So now were just looking at Sin(45 degrees)

Answer 19

Right. Since it goes in there evenly, we're back at the 2pi side? So we're in the first quadrant?

Answer 20

Correct, at 360,000 we've made (I think 1,000) complete circles. We have 45 left, so we start at 0 degrees again

Answer 21

Ohh. Okay. That makes sense, so we have (sqrt(2)/2, sqrt(2)/2)

Answer 22

Correct!, since we landed in the first quadrant and x, y are both positive

Answer 23

Whoo! I see where I had gone wrong, thank you!

Answer 24

You're welcome!