Question

y=-cos(x+π)+1

Answer 1

Need explanation... PLEASE!

Answer 2

what are you trying to do exactly?

Answer 3

I need to solve.

Answer 4

you need to give me an x value or do you want to find the roots?

Answer 5

I need a step by step explanation of how to solve it

Find the roots

Answer 6

I'm pretty sure for this problem you can use the trig identity
cos(x+h) = cos(x)cos(h) - sin(x)sin(h)
where h=pi

Answer 7

do you think you can solve it now that I have informed you of that trig identity?

Answer 8

I am still lost...

Answer 9

:(

Answer 10

I thought I understood it but then I got lost again...

Answer 11

so first thing to do use the trig identity to make this less complex
y=-cos(x+π)+1
knowing cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
y = -(cos(x)cos(pi) - sin(x)sin(pi)) + 1
=
y = -cos(x)cos(pi) + sin(x)sin(pi) + 1

Answer 12

can you solve this?

Answer 13

no...

Answer 14

ok then do you even understand how I used the identity?

Answer 15

I think I have an idea...

Answer 16

do you know what the unit circle is?

Answer 17

pi(180)... I think

Answer 18

no if I wasn't so tired I could explain this better but this is the unit circle

Answer 19

I am exhausted as well...

Answer 20

sin(x) = y
cos(x) = x

you input an angle into them and it will give you the x or y value.

Answer 21

what math course are you in and do you plan on taking calculus in university?

Answer 22

This is very embarrassing but I took calculus 5 semesters ago... lol

Answer 23

so you just forgot meh.

well you use the unit circle to solve these questions I can show you how to quickly memorize it if you want and how to use it to solve trig functions.

Answer 24

As far as trig identities goes you will just have to know the basic ones.

Answer 25

but I will just answer your question so
y = -cos(x)cos(pi) + sin(x)sin(pi) + 1
y = -cos(x)(1) + sin(x)(0) + 1
y = -cos(x)

Answer 26

oh crud I mean
y = -cos(x) + 1

Answer 27

wait I messed up (half asleep remember)
cos(x) = -1
so we need to find an angle that will make cos(x) output -1

Answer 28

so we look on the unit circle remembering cos(x) = x

Answer 29

x being a coordinate not a number

Answer 30

Is it okay if you could write it step by step again? I feel bad...

Answer 31

well it is a number but yeah

Answer 32

sure

Answer 33

so first thing to do use the trig identity to make this less complex
y=-cos(x+π)+1

knowing
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
we can change cos(x + pi)

y = -(cos(x)cos(pi) - sin(x)sin(pi)) + 1
=
y = -cos(x)cos(pi) + sin(x)sin(pi) + 1

look at the unit circle


cos(x) = x coordinate
sin(x) = y coordinate

so
cos(pi) = -1
sin(pi) = 0

so we have

y = cos(x) + 1

Answer 34

An easy way to memorize the unit circle is to remember the first slice pi/3, pi/4 and pi/6

then to remember the intergers ontop of the fractions on the othersides going counter clockwise

->2,3,5
4,5,7<-
->5,7,11

then to remember the coordinates just easy as going 1, 2, 3, squaring the numbers then dividing them by 2, and just doing the backwards on the bottom half of the circle. Then you just have to remember where to put the negatives but yeah

Answer 35

for the y coordinates you just do what I explained in the paragraph above only backwards.

Do you see how I solved this problem now?

Answer 36

and if you are done calculs why do you need to do this question?

Answer 37

Someone needed my help. LOL I feel ashamed that I am lost.

Answer 38

I would give you 10000 medals if I can...

Answer 39

well seeing as metals are worthless I don't mind that you cannot. Here is a sheet that might interest you as it touches on trig identites

Answer 40

Thank you very much for your help!

Answer 41

No problem glad to help

Answer 42

-cos(x+π)+1 = 0

-> cos(x+π) = 1
-> cos(x+π) = cos0
=> x+π = 0
=> x = π = 180°