Question

Almost done! I just have this problem and one more after that. I could really use some guidance with this one. A bit confusing for me. :/ Click attached

Answer 1

(1-cos(x))/sin(x) = sin(x)

1-cos(x) = sin(x)*sin(x)

1-cos(x) = sin^2(x)

1-cos(x) = 1-cos^2(x)

1-z = 1-z^2 ... Let z = cos(x)


Now solve for z

Answer 2

It's not matching up, I'm not getting it :/

Answer 3

What solution(s) are you getting for z?

Answer 4

How far did you get if you were unable to solve for z?

Answer 5

really what we have here is the set is answer three check me if I am right?

Answer 6

you there still?

Answer 7

Oh sorry, I left my computer for a bit. Oh, @godorovg how do you come to that conclusion?

Answer 8

(0, pi)

Answer 9

When you solve

1-z = 1-z^2

for z, what do you get?

Answer 10

I went over it again a got option three. Thank you for the help guys!

Answer 11

it's not option 3

Answer 12

Can you please go through it step by step with me then? I can't do this on my own :/

Answer 13

well we know 1-z = 1=z^2 is 1-z = (1-z x 1+z) I am on the right track?

Answer 14

if x = pi, then sin(x) = sin(pi) = 0, which is a no-no because we'll be dividing by zero

So x = pi isn't a solution (it's not even in the domain)

Answer 15

1-z = 1-z^2

1-z+z = 1-z^2 + z

1 = 1-z^2+z

1-1 = 1-z^2+z-1

0 = -z^2+z

-z^2+z = 0

-z(z-1) = 0

-z = 0 or z-1 = 0

z = 0 or z = 1

--------------------

We made z = cos(x), so

cos(x) = 0 or cos(x) = 1

Solve each for x


cos(x) = 0

x = arccos(0)

x = pi/2 or x = 3pi/2
-----------

cos(x) = 1

x = arccos(1)

x = 0

So the solution set is {0, pi/2, 3pi/2}

Answer 16

Oh, I see. Thank you @jim_thompson5910 for the explanation and clarification. I appreciate your help

Answer 17

np

Answer 18

I'm glad it's making sense now

Answer 19

oh wait, I'm not thinking...x = 0 doesn't work (for the same reason I explained above)

So it's just {pi/2, 3pi/2}

Answer 20

sry it's late over here lol

Answer 21

x = 0 isn't a solution because it causes a division by zero error

Answer 22

Oh lol it's fine. Thanks!

Answer 23

alright, yw