Trigonometry - 2015-12-30

Simple Art

02:45

Hello, please ask me what your concerns are.

Adan Ramirez

hii :D

Simple Art

:D

Adan Ramirez

check this link out, this is what i want to do:

wolframalpha.com/input/…

Simple Art

oh

Adan Ramirez

i want that new point, is ur answer in my OP doing that?

Simple Art

02:48

wolframalpha.com/input/…

Yes, my solution should work.

Adan Ramirez

for starters, what are the things you need to know when solving a problem like this?

Simple Art

You want a calculator for trig. functions

evaluating cosine, sine, etc.

Adan Ramirez

do i have to work with matrices?

Simple Art

Not necessarily, my answer doesn't have matrices

Adan Ramirez

in ur answer, what is r?

Simple Art

02:50

Matrices can simplify things down though

r is the distance from the pivot to your point you are rotating

Adan Ramirez

for example, x = rcos(angle)

Simple Art

given in the general r^2=x^2+y^2 using Pythagorean theorem

Adan Ramirez

you started with substitutions, x = rcos(angle)

Simple Art

My method is particularly simple

Adan Ramirez

what do we do with that distance?

i want to know ur train of thought behind all of htis

Simple Art

02:52

Multiply it after we rotate

rotating won't affect distance from origin/pivot

Get it?

I solved mine similar to De Moivres' method

Adan Ramirez

y = rsin(agnle) is doing the same thing?

Simple Art

yes, rotating with the distance part factored out

very easy with a calculator

Adan Ramirez

so if my angle is 45degrees, i use: x = rcos(45)?

Simple Art

Sort of

Adan Ramirez

x1 is x prime?

Simple Art

02:56

We use x = r*cos(45+rotation)

x1 is first x coordinate

x1+y1=A?

Adan Ramirez

yes

4,5

Simple Art

for A, x1=4, y1=5

Adan Ramirez

how do we get r?

Simple Art

find distance from (4,5) using Pythagorean theorem

or distance formula

Adan Ramirez

(4,5) and (4,1)?

Simple Art

02:58

distance would be r = 4

Adan Ramirez

ok just making sure

Simple Art

np

This place can really be nice, private tutors for free and all (except the tutorers here are very smart)

Adan Ramirez

to calculate x1 = 4cos(45 + pi/4)?

i bet they are smart, this stuff is so new to me, im used to geometry

Simple Art

Um, wait

Adan Ramirez

and x1 is the point we looking for?

Simple Art

03:00

x1 = 0*cos(stuff)

distance from A to (4,5) = 0

Are we talking about B?

er, I mean C?

Adan Ramirez

nooo dont confuse me

hah

A = 4,5, B = 4,1

Simple Art

ok

Adan Ramirez

d = 4

Simple Art

well

Adan Ramirez

x1 = 4 * cos(45 + pi/4)?

Simple Art

03:02

we are comparing the distance to the pivot point

that is, the point we are rotating around

Adan Ramirez

hmmm

x != x1?

we comparing B to x1?

Simple Art

yup

wait, slow down

Imagine trying to rotate (0,0) around (0,0)

Adan Ramirez

d = 0

Simple Art

The distance from pivot is r = 0

right, so there should be no change afterwards

Adan Ramirez

so x has to = x1?

Simple Art

03:05

mhm...

that is just for A

For B, we have d = 4

and (from stuff), theta = 270

say we want to rotate it 30 degrees

so we now have: theta = 300

Adan Ramirez

angle = theta?

the symbol

Simple Art

yeah

for our new x value, we have x = 4*cos(300)

but then....

we have to remember to add 4 to our x

because we rotated it around ("4",5)

so it is x=4*cos(300)+4

Adan Ramirez

what i did was : x = 4 * cos(45) = 2.101, x1 = 4 * cos (45 + pi/4) = -.92088, x is not x1

Simple Art

plug into calculator

well, you have to actually find the old angle

which you can use trigonometry for

Adan Ramirez

i got 3.9116

Simple Art

03:09

That is probably right for mine

but I rotated it 30 degrees

Adan Ramirez

that 1 is urs, but now im confused

Simple Art

one second

When I said x=x1, I was talking about "A"

Adan Ramirez

all i know is (4,5) to (4,1) = 4, the rotation is 45degrees

Simple Art

A=(4,5)

right...

Adan Ramirez

i dont know what to do from there

Simple Art

03:11

but what do you want to rotate around what?

Adan Ramirez

4,5 rotate 45degrees

a-b

wolframalpha.com/input/…

how do i start?

Simple Art

You want to rotate (4,1) around (4.5) by 45 degrees

Adan Ramirez

there we go yes

Simple Art

We know d = 4

we know the angle/theta is 270 (from some trigonometry or looking at a graph)

oh, wait

Adan Ramirez

how did u get 270?

Simple Art

03:13

let me tell you how I found it

0 degrees equals right

90=up

180=right...

270=down

Adan Ramirez

180= left?

Simple Art

yeah, my bad

Adan Ramirez

:3

270 is down

and 360 = right

Simple Art

We see that 4,1 is directly down, below 4,5

so 270 degrees

Adan Ramirez

quadrant IV?

Simple Art

03:14

If its somewhere else, trigonometry, something I can't explain

No, note quadrants, just where 4,1 is in relation to 4,5

Adan Ramirez

so we know it's 270

Simple Art

yes

r=4

Adan Ramirez

isnt it in 0-90?

Simple Art

?

Adan Ramirez

4,5 and 4,1 are in the first quadrant where 0->90

Simple Art

03:15

Um, I believe we just proceed as follows:

Adan Ramirez

hmm so i have to know more stuff to understand how u got 270?

Simple Art

no, we are looking at 4,1

no, no, no

look at 4,1 on a graph

look at 4,5 on the same graph.

4,1 is simply directly below 4,5

If I leave randomly, its because my mom said so and its late...

Adan Ramirez

is that wrong? it looks like 4, -1

are we reversing y?

Simple Art

no...

Adan Ramirez

(-y , x) (x, y)?

why in the graph is 4, 1 located below the x axis tho?

Simple Art

03:18

(4,1) is below (4,5), do you get that much?

Adan Ramirez

ofc

Simple Art

that's really all we need to know it is 270 degrees

Adan Ramirez

ok deal

Simple Art

:D and we have d=4

Adan Ramirez

that'l be homework for me, so continuing on

Simple Art

03:19

ok, this part gets tricky if you don't really pay attention

You can rejoin this room later and I'll receive notifications btw

Look at the x values for (4,1) and (4,5)

Adan Ramirez

ok np, kk

Simple Art

The x values are the same, so we say x=0

Adan Ramirez

ok

Simple Art

The y values are 4 less, so y=-4

Adan Ramirez

1-5?

Simple Art

03:21

yeah

Adan Ramirez

ok

Simple Art

we know 0=4*cos(270)

and - 4=4*sin(270)

That is simply our x/y values and plugging in the knowns/found

Our new x value will be x1=4*cos(270+45)

our new y value will be y1=4*sin(270+45)

Adan Ramirez

2.666766240158

Simple Art

=x

Adan Ramirez

y = 2.98053305823

Simple Art

03:23

ok

Adan Ramirez

and that's it?

Simple Art

wait, you messed up

Set your calculator to degrees mode

Adan Ramirez

oops :D

x = 2.82842712475

Simple Art

don't do y, I don't have time

Adan Ramirez

fk

T_T

Simple Art

03:25

2.82842712475 is the amount right of (4,5)

Adan Ramirez

y = -2.82842712475

ok

Simple Art

-2.82842712475 is the amount down from (4,5)

Adan Ramirez

mhm

Simple Art

So our new point should be (4+2.82842712475 ,5-2.82842712475)

Put that into your calculator and your done

Adan Ramirez

omg

Simple Art

03:26

yes?

Adan Ramirez

got it

ty :D

Simple Art

its that easy. (not sure what that means)

note that it will simply be harder to find the angle if it is not up/down, left/right

Adan Ramirez

true

can we go over that tomorrow?

if u have time :D

Simple Art

Ask someone else on that topic, I have to go for tonight (don't ask it on this site, they'll downvote you like crazy)

I always find time

Adan Ramirez

okay :D thanks again

Simple Art

03:28

If you leave messages here, I will respond.

Adan Ramirez

kk

Simple Art

Ta Ta for now!

Adan Ramirez

cya

Transcript for

$Mathematics$ Trigonometry