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JayDS
Group Title
Solve the following equations over [0°, 360°].
1) 2 sin (x − 60)° = 1
2) √2 cos(x+90)°+1 = 0
Show working out thanks.
 one year ago
 one year ago
JayDS Group Title
Solve the following equations over [0°, 360°]. 1) 2 sin (x − 60)° = 1 2) √2 cos(x+90)°+1 = 0 Show working out thanks.
 one year ago
 one year ago

This Question is Closed

Callisto Group TitleBest ResponseYou've already chosen the best response.1
For question (1) 2 sin (x − 60)° = 1 Divide both sides by 2, what do you get?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
sin(x60)°=1/2
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Yes. Next, take arcsine for both sides, what do you get?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
sorry, what's arcsine?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
opposite of sine?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
arcsine is the inverse of sine function.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
(x60)°= sin1 (1/2)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Yes. What does \(sin^{1}\frac{1}{2}\) give you?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Yes. That's the angle in quadrant I, what about in quadrant IV?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
36030=330 deg
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Or it's the good habit to memorize 1/2 = sin 30
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
I do remember it actually.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Oh~ So.. you get x  60 = 30 or x60 = 330 Can you solve the two?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
x=90 or x=390
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Ah!!! My mistake!! The other angle should be in quadrant II... Since sine is positive in quadrant I and II.. I'm sorry!!
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
I'm sorry... Just start it again! For question 1, 2 sin (x − 60)° = 1 Divide both sides by 2, which you've done just now. sin (x − 60)° = 1/2 Take arcsine for both sides, you get x60 = 30 or x60 = ______ (____is the angle in quadrant II, since sine of a angle in quadrant I and II gives you a positive value)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Can you work out the ___ ?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
Would it be 90?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Hmm.... We're still on x60 = (angle in quadrant II), right?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yeh but I'm a bit confused with your method.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
on that step.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
how I was taught to do it was to find the angle in the first quadrant first, in this case it is 90 I believe?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
and then using the angle that you found you use 180that angle found= to get the answer
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Can we do it in this way? Solve siny = 1/2, what is/ are y?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
y= sin^1 (1/2)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
which is equal to?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Right! So, you get y=30 or y=150, agree?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Now, back you your question. 2 sin (x − 60)° = 1 sin (x60) = 1/2 So, in this case, let x60 = y, you'll get siny = 1/2. and just now, you solve y, which is 30 or 150. So can you get x?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
x60=30 or x60=150 x=90 or x= 210
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Now, it's done~
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yeh but I'm still a bit confused with a part of it.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Which part?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
near the last part?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
What is it exactly?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
"So, in this case, let x60 = y, you'll get siny = 1/2. and just now, you solve y, which is 30 or 150. So can you get x?"
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
wait, is it possible if u type out all the working out in logical order?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Oh... perhaps I should write it in this way. 2sin(x60) = 1 Let y = x60, then the equation becomes 2siny = 1 So, siny = 1/2 And as what you did, y= 30 or y=150 So, replace y by x60 x60 = 30 or x60 = 150 Solve x. It should be clearer now. Please ask if you still have questions. And sorry for my poor presentation just now :(
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Or you can visualize the circle: 1/2 = sin30 = sin ( 180  30 )
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
kk, I get the working out but yeh I may not remember how to do it your way as I was sort of taught a different way by my cousin and I absolutely hate these type of confusing type questions.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
It's okay. Just choose the best way for yourself. :) Can you do question 2?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yep, well I'll try do it your way and I think I can only do half of the steps
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
You can try to do it using your own way first :)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
I'll check it for you
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
wait, so I've done this so far using your method, the rest I don't get. √2 cos(x+90)°+1 = 0 cos(x+90)° = 1/√2 let y = x + 90 therefore cos y = 1/√2 y = ............ or y = ............
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
So far so good :) What are the values of y such that cosy = 1/√2
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Hint: 1/√2 = √2/ 2
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Hmm.. Forget my method... Can you solve it using your OWN way??
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
well it was my cousin's way and he only taught me just then. I still don't quite fully understand his method that's why I was planning to see if anyone could simplify it down for me on here.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Can you do me a favour by showing how your cousin has taught you? You can use another question or simply this question if you like.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
tan (x+45°) = 1 x∈[0°,360°] x+45 = 45° (x+45°) ∈ [45°,405°] 180° + 45° or 405° x+45° = 45°, 225° or 405° x = 0°, 180° or 360°
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Your cousin's way is exactly as same as our way!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
lol, really?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
I hope you don't mind me asking the following question. 1. Have you learnt CAST ? 2. Do you know something like cos(180  x) = cosx sin(180x) = sinx and so on? 3. Are you familiar with the trigo functions of special angles (that are 0 , 30 , 45, 60, 90, and so on) ? It's practically the same
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yes, I have and I do know the trig functions that u mentioned
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Oh great. Sudden quiz. What is cos135?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
in exact value or degrees?
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Hint: 135 < 180
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
135 is in degrees. cos135 gives you an exact value.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
cos45 = Sqrt2/2
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Can we go back to your question 2 now?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yes, please. It's late over here and I want to go to sleep lol.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
but I want to figure out how to do it properly first so I can do the other ones tomorrow.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Don't worry, I have to do my quiz in an hour too : Here's your work! √2 cos(x+90)°+1 = 0 cos(x+90)° = 1/√2 let y = x + 90 therefore cos y = 1/√2 Can you solve y now?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
wait. let me see... and good look for your quiz.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
well since the value is negative it has to be in the second or third quadrant?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Yes. Another hint given by @Chlorophyll before : 1/√2 =  (1/√2) x (√2/√2) =  √2/2
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
from there I'm a bit stuck as to how to solve for y.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Consider y as X!
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
cosy = √2/2 What is the value of angle such that cos(angle) = √2/2? Another hint: refer to the sudden quiz
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yes, but how did you get the √2/2?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Ratinoalization?! 1/√2 =  (1/√2) x (√2/√2) =  √2/2
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
can't u cancel the top and bottom Sqrt 2 and so u get 1/Sqrt2
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Oh yes, of course! But you need to know that cos45 = 1/√2
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
√2/2 looks more familiar to you or not?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yes, it is cos 45 right?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
cos 45 in this case*
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
cos45 = cos(___ 45) = cos(____+45) ?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
cos45 = cos(18045) = cos (180+45)?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Yes. So... cosy = 1/√2 y = ... or y= ...?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
wait... let me write something else down first.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
Take your time~
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
@JayDS @Callisto giant leap improvement here =)
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
lol, no way, I haven't improved at all but Callisto has.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
What??!!! You haven't improved at all :'( ???
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
√2 cos(x+90)°+1 = 0 cos(x+90)° = 1/√2 let y = x + 90 therefore cos y = 1/√2 cos y =  √2/2 hmm where to from here?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
I guess I have slightly lol, I'm just really stupid.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
@JayDS Our goal here is to help YOU improved :)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
No one is stupid except me, you can't be stupid than me: √2 cos(x+90)°+1 = 0 cos(x+90)° = 1/√2 let y = x + 90 So, the equation becomes cos y = 1/√2 Your duty: solve y. How...?!
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
*delete ''you can't be stupid than me''
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
haha thanks, I guess I'm just a logical person, like I things shown out clearly well in a way that I can understand of course and I'm slow at learning, well depends on what type of maths as well.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
@Callisto wanna me to take over so you have time with your quiz?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
sorry for taking up your time guys and thanks for your help so far.
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
@Chlorophyll Ah... I forget my quiz : I'll come back as soon as possible!!
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
@Callisto Good luck, Sis! Not to be worried I promise to a good job here :)
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.1
@Chlorophyll Sis, I trust you :) Thanks too!!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
what's with the "Sis" lol
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
√2 cos(x+90)°+1 = 0 > cos(x+90)° = 1 /√2 = √2/2 Since cos value is negative, now replace ... into where √2/2 is, can you!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
sorry, I'm confused about the replacing part.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Hint: the angle in the second and third quadrants
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yep, I know that but... I'm unsure how to use that
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
second quadrant = pi  angle so it will be pi  sqrt2 /2 third quadrant = pi + angle so it will be pi + Sqrt 2/2 Is that correct?
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
cos(x+90)° = √2/2 cos(x+90)° = cos45 = cos(18045) = cos (180+45)
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
So you have 2 cases here!
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
x+90° = 18045 and .....
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yeh, that is the same as what I said earlier? pi  sqrt 2/2 and pi + sqrt 2/2 I believe.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
but then you would need to convert is back to degrees.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
It's incorrect to connect the degree ( pi) with the radian ( arc length ) pi  sqrt 2/2
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
kk, can you quickly explain this line "cos(x+90)° = cos45 = cos(18045) = cos (180+45)"
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
oh wait, I think I got it.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Don't pay attention to the left part yet!
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
√2/2 = cos45 Now we wish to get rid of negative sign: cos45 = cos ( 180  45) cos45 = cos ( 180 + 45)
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
That's what Callisto has been working so hard to show you the concept!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
√2 cos(x+90)°+1 = 0 cos(x+90)° = 1/√2 let y = x + 90 So, the equation becomes cos y = 1/√2 cos y = √2/2 cos y = cos 45 cos (x+90) = cos 45 cos45 = cos ( 180  45) cos45 = cos ( 180 + 45)
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Actually now you've done with the right side, plug it into the equation: cos (x+90) = cos 45 In the second quadrant: cos (x+90) = cos ( 180  45) > x+90 = ....?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
x + 90 = 135???
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
> x = ...?
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Similarly for the third quadrant case, can you do it yourself?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
well if x=45 wouldn't it just be 180+45=225?
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
cos (x+90) = cos ( 180 + 45) > x+90 = ....?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
x + 90 = 225 x = 135
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
I suggest that you don't jump around, as we carefully show you step by step, just follow it one by one, and practice it yourself from now on!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
LOL, okay big sis ^^ I will practice tomorrow but it's getting late so I'm going to sleep now.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Okie, the solution already saved into your profile. Feel free to use it as your study note!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
really, how?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
is that a new function?
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Click into your profile, you'll see all your questions and answers!
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
You can't see your own questions and answer in your profile?
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
Maybe you can only do because you have already reached 99 smart points or something.
 one year ago

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
No, you can check anybody profiles!
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
yeh kk, found it, it was on the left side, I didn't see it over there and I thought you couldn't click anything there.
 one year ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
Well I g2g now Sis, thanks so much for the help and help me say thanks to Callisto as well.
 one year ago
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