Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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.
 2 years ago
 2 years 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.
 2 years ago
 2 years 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?
 2 years ago

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

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

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

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

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

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

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

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

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

JayDS Group TitleBest ResponseYou've already chosen the best response.0
I do remember it actually.
 2 years 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?
 2 years ago

JayDS Group TitleBest ResponseYou've already chosen the best response.0
x=90 or x=390
 2 years 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!!
 2 years 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)
 2 years ago

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

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

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

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

JayDS Group TitleBest ResponseYou've already chosen the best response.0
on that step.
 2 years 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?
 2 years 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
 2 years 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?
 2 years ago

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

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

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

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

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

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.1
What is it exactly?
 2 years 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?"
 2 years 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?
 2 years 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 :(
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.1
*delete ''you can't be stupid than me''
 2 years 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.
 2 years 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?
 2 years 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.
 2 years 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!!
 2 years 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 :)
 2 years ago

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

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

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

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

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

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

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

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

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

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
Don't pay attention to the left part yet!
 2 years 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)
 2 years 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!
 2 years 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)
 2 years 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 = ....?
 2 years ago

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

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

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

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

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

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

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

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

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

Chlorophyll Group TitleBest ResponseYou've already chosen the best response.1
No, you can check anybody profiles!
 2 years 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.
 2 years 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.
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.