Question

Without using a calculator, find the exact value of arccos (cos(17pi/5)). Justify answer, thanks. An explanation would be helpful.

Answer 1

hi @joselin12

Answer 2

this one is fairly easy being that arccos and cos are inverses of each other. It be like finding the squareroot of 2 squared is 2

Answer 3

Hey, so do they cancel?

Answer 4

yes (math people hate the word cancel) but yes

Answer 5

Haha so the answer is just 17 pi/5

Answer 6

but hang on...

Answer 7

17pi /5 has something tricky about it i think... because its not in the domain of arccos

Answer 8

its bigger than 2pi

Answer 9

Yeah

Answer 10

So you need to find the corresponding angle in the same quadrant (aka subtract 10Pi/5)

Answer 11

How did you find that?

Answer 12

(10/5)Pi = 2Pi

Answer 13

2pi radians is a whole circle, so you just go around the circle until you're in the domain of the unit circle

Answer 14

Oh okay

Answer 15

So 7 pi/5

Answer 16

I think so

Answer 17

grr it has to be between [-pi/2, and pi/2] for sine and cosine

Answer 18

so in other words, in the first or fourth quadrant

Answer 19

(7/5)Pi is in the second quadrant.

Answer 20

ok i think i can explain, you still there?

Answer 21

its a bit tricky, but i think i can explain.

Answer 22

The range of cosine is from 0 to pi so wouldn't it be 3pi/5

Answer 23

yes its 3pi/5

Answer 24

Since 7pi/5 isn't in the range right..

Answer 25

17Pi/5 is in quadrant 2. 3pi/5 has the same cosine value but is in quadrant 1. does that make sense?

Answer 26

The domain of arccos and arcsine is -pi/2,pi/2

Answer 27

oh crap I'm looking at arcsin; you're correct i'm wrong. the domain for arccos is 0 to pi and 7pi/5 is greater than pi

Answer 28

Kind of I just don't get how you know what quadrant they're located on

Answer 29

ok one sec, that's easy

Answer 30

17pi/5 is in quadrant 3 .

Answer 31

How do you know

Answer 32

one sec