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For question (1)
2 sin (x − 60)° = 1
Divide both sides by 2, what do you get?

sin(x-60)°=1/2

Yes. Next, take arcsine for both sides, what do you get?

sorry, what's arcsine?

opposite of sine?

arcsine is the inverse of sine function.

(x-60)°= sin-1 (1/2)

sin^-1

Yes. What does \(sin^{-1}\frac{1}{2}\) give you?

30

Yes. That's the angle in quadrant I, what about in quadrant IV?

360-30=330 deg

Or it's the good habit to memorize 1/2 = sin 30

I do remember it actually.

Oh~
So.. you get
x - 60 = 30 or x-60 = 330
Can you solve the two?

x=90 or x=390

kk

Can you work out the ___ ?

Would it be 90?

Hmm....
We're still on x-60 = (angle in quadrant II), right?

yeh but I'm a bit confused with your method.

on that step.

and then using the angle that you found you use 180-that angle found= to get the answer

Can we do it in this way?
Solve siny = 1/2, what is/ are y?

y= sin^-1 (1/2)

which is equal to?

30

and?

150?

Right!
So, you get y=30 or y=150, agree?

yeh

x-60=30 or x-60=150
x=90 or x= 210

Now, it's done~

yeh but I'm still a bit confused with a part of it.

Which part?

near the last part?

What is it exactly?

wait, is it possible if u type out all the working out in logical order?

Or you can visualize the circle:
1/2 = sin30 = sin ( 180 - 30 )

It's okay. Just choose the best way for yourself. :)
Can you do question 2?

yep, well I'll try do it your way and I think I can only do half of the steps

You can try to do it using your own way first :)

I'll check it for you

So far so good :)
What are the values of y such that cosy = -1/√2

not sure

Hint: -1/√2 = -√2/ 2

Hmm.. Forget my method...
Can you solve it using your OWN way??

Your cousin's way is exactly as same as our way!

lol, really?

yes, I have and I do know the trig functions that u mentioned

Oh great.
Sudden quiz. What is cos135?

in exact value or degrees?

Hint: 135 < 180

135 is in degrees.
cos135 gives you an exact value.

-cos45 = -Sqrt2/2

Yes.

Can we go back to your question 2 now?

yes, please. It's late over here and I want to go to sleep lol.

but I want to figure out how to do it properly first so I can do the other ones tomorrow.

wait. let me see... and good look for your quiz.

well since the value is negative it has to be in the second or third quadrant?

Yes. Another hint given by @Chlorophyll before : -1/√2 = - (1/√2) x (√2/√2) = - √2/2

from there I'm a bit stuck as to how to solve for y.

Consider y as X!

yes, but how did you get the -√2/2?

Ratinoalization?!
-1/√2 = - (1/√2) x (√2/√2) = - √2/2

can't u cancel the top and bottom Sqrt 2 and so u get -1/Sqrt2

Oh yes, of course! But you need to know that cos45 = 1/√2

-√2/2 looks more familiar to you or not?

yes, it is cos 45 right?

-cos 45 in this case*

-cos45 = cos(___ -45) = cos(____+45) ?

-cos45 = cos(180-45) = cos (180+45)?

Yes. So...
cosy = -1/√2
y = ... or y= ...?

wait... let me write something else down first.

Take your time~

lol, no way, I haven't improved at all but Callisto has.

What??!!! You haven't improved at all :'( ???

I guess I have slightly lol, I'm just really stupid.

*delete ''you can't be stupid than me''

I like*

sorry for taking up your time guys and thanks for your help so far.

@Chlorophyll Ah... I forget my quiz :| I'll come back as soon as possible!!

@Chlorophyll Sis, I trust you :) Thanks too!!

what's with the "Sis" lol

sorry, I'm confused about the replacing part.

Hint: the angle in the second and third quadrants

yep, I know that but... I'm unsure how to use that

cos(x+90)° = -√2/2
cos(x+90)° = -cos45 = cos(180-45) = cos (180+45)

So you have 2 cases here!

x+90° = 180-45 and .....

yeh, that is the same as what I said earlier? pi - sqrt 2/2 and pi + sqrt 2/2 I believe.

but then you would need to convert is back to degrees.

It's incorrect to connect the degree ( pi) with the radian ( arc length )
pi - sqrt 2/2

kk, can you quickly explain this line "cos(x+90)° = -cos45 = cos(180-45) = cos (180+45)"

oh wait, I think I got it.

Don't pay attention to the left part yet!

That's what Callisto has been working so hard to show you the concept!

x + 90 = 135???

-> x = ...?

45

Similarly for the third quadrant case, can you do it yourself?

well if x=45 wouldn't it just be 180+45=225?

cos (x+90) = cos ( 180 + 45)
-> x+90 = ....?

x + 90 = 225
x = 135

LOL, okay big sis ^^ I will practice tomorrow but it's getting late so I'm going to sleep now.

Okie, the solution already saved into your profile. Feel free to use it as your study note!

really, how?

is that a new function?

Click into your profile, you'll see all your questions and answers!

You can't see your own questions and answer in your profile?

Maybe you can only do because you have already reached 99 smart points or something.

SmartScore*

No, you can check anybody profiles!

Well I g2g now Sis, thanks so much for the help and help me say thanks to Callisto as well.