Trigonometry - The Unit Circle

[civic crag]

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[snow plover]

...is 210 divisible by 30?

What's 210 + 30? What about 210 - 30?

[final dock]

The answer on the answer sheet was like cos(210)= -cos(30)

[snow plover]

Right, and I'm trying to help you understand why.

[final dock]

Ooh

[snow plover]

So what's 210 - 30?

[final dock]

180

[snow plover]

Therefore cos(210 deg) = cos(180 deg + 30 deg), right?

[final dock]

Yea

[snow plover]

So now we use the angle sum formula.

[final dock]

What’s the formula

[snow plover]

Wait, were you not taught it yet?

[final dock]

Well im not aware of smth called ‘angle sum formula’

Unless they worded it differently or call it smth else..

[snow plover]

cos(a + b) equals what?

[final dock]

Yea haven’t learnt that 😭

[snow plover]

...okay, then.

Well, let's just look at the unit circle.

[snow plover]

See how the right triangle is a 30-60-90?

[final dock]

What’s a 30-60-90

[snow plover]

...a triangle with angle measures 30 degrees, 60 degrees, and 90 degrees...

[final dock]

OH MB

Right right

Yea

Sorry im slow 😭

[snow plover]

So then note that point p there is (cos(210 deg), sin(210 deg)), right?

[final dock]

Yea

[snow plover]

But also, how far is it to the left?

[final dock]

The length ?

[snow plover]

Yes.

[final dock]

-0.87

[snow plover]

Okay, but exactly how far is it?

[final dock]

So no rounding?

[snow plover]

Yes.

[final dock]

-0.8660254038

[snow plover]

that's still rounded because it's irrational.

[final dock]

Well thats what its saying on the calculator im not sure how else im supposed to get the answer 😭

[snow plover]

Look at the triangle.

[final dock]

?

[snow plover]

What are you putting in to the calculator?

[final dock]

Cos(210)

[snow plover]

Okay, don't put anything into any calculators.

The point here is for you to understand intuitively why it comes out like this.

[final dock]

Well i feel like sicne we’re allowed to use a calculator on the exam i think that it doesn’t rlly matter because they wont mark e down for that

All im trying to figure out is the answer to this and how to do it

[snow plover]

If you don't understand the problems, the calculator won't help you.

[final dock]

I understand what it’s asking me to do… when it says determine what cos(210) is

And my teacher said to put it into a calculator to get the answer

The only thing that i need to know is if the answer will be a positive or a negative number/decimal

[snow plover]

Saying that you understand it when it says something it doesn't say isn't saying you understand it.

[snow plover]

That's not the only thing you need to know.

[final dock]

Wdym when it says smth it doesn’t say 💀

[snow plover]

The question doesn't say "determine what cos(210 deg) is".

So saying that you understand it when it says that is meaningless because it doesn't say that.

[final dock]

Thats the question above.. it says determine what cos(210) is and that got me -0.87…

And i did that question and got the answer right

Now its this question im stuck on

[snow plover]

What was part a?

That's not the same question.

[final dock]

Mb

Question 10

[snow plover]

I'm not sure how you're supposed to use the circle to determine anything.

[final dock]

Thats not the question im stuck on dude 😭

It’s question 10) c. That i need help with

[snow plover]

Unless you were already taught the trig ratios of a 30-60-90 triangle.

[final dock]

?

[snow plover]

...what is there to question about that?

[final dock]

Im questioning why are u telling me this

Im not asking how to use the circle to determine the value of cos(210)

[snow plover]

Maybe you should be.

[final dock]

Why would i be asking that when i literally got the answer right ☠️

[snow plover]

You didn't get anything right, your calculator did.

[final dock]

Bro if u cant help with question 10) c and 10) e. Then don’t help at all 💀

Im literally doing 10th grade math theyre not gonna make me figure out that stuff by myself

Bc we can use a calculater on the test

[snow plover]

See, I'm trying to help you, but you don't seem to want to learn.

[final dock]

Coz I don’t want to learn what ur trying to help me rn 😭

I WANT to learn what I ASKED to learn

Which is question 10) c.

And e

[snow plover]

And I'm trying to teach you that, but to teach you that I need to teach you this.

[final dock]

No u don’t, I don’t need to know how to calculate cos(210) in my head when i can use a calculator that I WILL be using on my mid yearly exams

[snow plover]

How do you know what you do or don't need to learn in order to learn something you don't know?

[final dock]

Bc it’s grade 10 math.

[snow plover]

And that allows you to know everything about everything you don't know?

[final dock]

If the only way to do question c was to calculate cos(210) in our head then they would not give us this question

And the answer seems pretty straight up and not complicated I just don’t know HOW to get to the answer and im sure it’s like a 2 step process

[snow plover]

I know you don't know how to get the answer. That's what I'm trying to explain but you won't let me.

[final dock]

☠️

Ight go explain it I’ll let u

Go ahead

[snow plover]

Okay. So here's the thing. The trig ratios of a 30-60-90 triangle are actually really easy to determine.

Here's how.

First, draw an equilateral triangle with side length 2.

An equilateral triangle has all three angles 60 degrees, right?

[final dock]

Yea

[snow plover]

So then you just bisect one of those angles.

Which also is the perpendicular bisector of the opposite side.

Now you have a 30-60-90 triangle with hypotenuse 2 and one leg of length 1.

So what's the length of the other leg?

Just use the Pythagorean theorem.

What answer did you get?

[final dock]

Thats literally the answer…

It wasn’t that deep😭

[foggy gust]

... for the calculator. It still eludes you.

[final dock]

I wasn’t asking how to calculate the cos(210) by myself, it’s not needed at my math level

Why is that so hard for u guys to understand ☠️

As long as i put the right equation in the calculator

[foggy gust]

Knowing the value of trigonometric ratios (edit: of special angles) is 10th grade syllabus

[final dock]

Well not here it’s not

[foggy gust]

Where are you from?

You don't need to be specific, it is just so that we can identify the syllabus

Even better if you can name the public exam you will be facing

[fluid pelican]

its just cos(pi + 30)

pi is odd

so answer is -cos(30)

[final dock]

Thank you

[hushed crane]

@final dock has given 1 rep to @fluid pelican

[foggy gust]

What?

[fluid pelican]

its a trick

if pie is even or odd then you don't have to change sin

if its in fraction you have to change

[foggy gust]

The mixture of radians and degrees without any specification...

[fluid pelican]

cos(180 + 30)

[foggy gust]

You mean the number of copies of pi added... pi isn't even an integer, what even is its parity?

[fluid pelican]

cos (2 x pi/2 + 30)

cos (pi +30)

[fluid pelican]

i don't understand your question

[foggy gust]

Neither do I understand "pi is odd"

[fluid pelican]

if coeffecient of pi is odd or even

sin wont turn into cos

[foggy gust]

Now, something comprehensible

[fluid pelican]

in this case its odd

it lies in -x axis (imaginary)

theta is +30 so it will move anti-clockwise

[foggy gust]

Again, what?

[fluid pelican]

theta is positive

[foggy gust]

Yes

[fluid pelican]

my bad

whenever angle is positive it means its moving anti clockwise

[foggy gust]

Yep I'm following

[fluid pelican]

so the angle is formed roughly in 3rd quadrant

cos is negative in it

[foggy gust]

Nope, it is in the third

[fluid pelican]

anyways

[foggy gust]

Your explanation up to this point is alright

[fluid pelican]

-cos(30)

[foggy gust]

Just that OP didn't want to know

anything about it

[fluid pelican]

oh

i was just shwing him instead of doing it in decimals

youu can do it in 2 steps

[foggy gust]

You can see Techie trying to introduce trig ratios of 30 deg and 60 deg above

But OP insisted that typing into calculators will suffice for their 10th grade syllabus

That's when I asked which syllabus

[fluid pelican]

oh