Question

Find all x and y (0 ≤ x, y < 2π) so that the following equation is true. (For each x and y enter answers from smallest to largest x-value.)
cos (x) + i sin (y) = sin (x) + i

Answer 1

so can you set the real parts and the imaginary parts equal to each other?

Answer 2

ok so here. I separated real numbers from imaginary... like text tells us to. i got... cos(x)=sin(x) and sin(y)=1.... so then i thought x would be sqrt2/2 and y = 1... and its not working for me

Answer 3

yes... thats what i just wrote above

Answer 4

hmm, well, sine of what number =1?

Answer 5

90 degrees?

Answer 6

in terms of pi?

Answer 7

pi/2

Answer 8

cool, so is there any other way that the sin y=1 other than y=pi/2?

Answer 9

on 0<y<2pi

Answer 10

well no bc 270 degrees = -1

Answer 11

good, so yes that is the only possible y value

Answer 12

now we need sin x= cos x

Answer 13

so isnt that sqrt2/2 which is pi/4

Answer 14

so if you graph sine and cosine on 0<x<2pi, where do the graphs intersect?

Answer 15

I am willing to bet they intersect more than once

Answer 16

ok, so sqrt 2/2 is 1/sqrt 2 yes? but that isn't an angle so the sine cannot be that

Answer 17

3pi/4

Answer 18

try graphing, it makes life way easier

Answer 19

hint: sin and cos can have the same signs in quadrant 1 and also in ?

Answer 20

nice hint choice

Answer 21

yeah so 3pi/4 or is that wrong?

Answer 22

which quadrant is 3pi/4 in?

Answer 23

3

Answer 24

let me see first, but here is y preference http://www.wolframalpha.com/input/?i=sinx%3Dcosx+solve+for+x&lk=4&num=1

Answer 25

so 3pi/4 isn't in quadrant 3

Answer 26

because it is less than pi which is less than 180

Answer 27

but I agree something in quadrant 3 should do the trick

Answer 28

check your angle again, I think the mistake may just be miscopying

Answer 29

i dont get it

Answer 30

ok, so 3/4 is less than one right?

Answer 31

ooo i meant 5pi/4

Answer 32

that would make more sense, let me see if that works :)

Answer 33

yep! that is it, see told you I thought it was a type-o :)

Answer 34

but... i dont know how to put in the answer bc everytime i put it in its wrong

Answer 35

what are you typing exactly?

Answer 36

at first i did exact value. then i answered with pi... still wrong.. unless i am typing in the wrong answer

Answer 37

ok
so
(x,y)
the smallest x was pi/4
the largerst x was 5pi/4
for either one of those the y will have to be pi/2
so the points (x,y) from smallest x to largest x:
(pi/4,pi/2)

(5pi/4,pi/2)

Answer 38

is that what you have been entering?

Answer 39

if not, take a picture of it and post it here so fibo and i can see it.

Answer 40

I think the way freckles said it should work

Answer 41

wait why? im confused.

Answer 42

you need an ordered pair, a set of x and y, not just one or the other

Answer 43

ok ok i understand