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

This Question is Closed

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

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

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

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. That's the angle in quadrant I, what about in quadrant IV?

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

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

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

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1I'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)

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

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

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

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0and then using the angle that you found you use 180that angle found= to get the answer

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

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Now, 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?

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0yeh but I'm still a bit confused with a part of it.

JayDS
 2 years ago
Best 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?"

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0wait, is it possible if u type out all the working out in logical order?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Oh... 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 :(

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0kk, 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.

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

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

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0wait, 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 = ............

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

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

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0well 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.

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Can 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.

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0tan (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°

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1I 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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0yes, I have and I do know the trig functions that u mentioned

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

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1135 is in degrees. cos135 gives you an exact value.

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0yes, please. It's late over here and I want to go to sleep lol.

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1Don'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?

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0well since the value is negative it has to be in the second or third quadrant?

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0from there I'm a bit stuck as to how to solve for y.

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

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

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

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

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

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

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

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

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

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

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

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

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

JayDS
 2 years ago
Best 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?

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

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1No 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...?!

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1*delete ''you can't be stupid than me''

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0haha 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.

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1@Callisto wanna me to take over so you have time with your quiz?

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0sorry for taking up your time guys and thanks for your help so far.

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.1@Chlorophyll Ah... I forget my quiz : I'll come back as soon as possible!!

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

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

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

Chlorophyll
 2 years ago
Best 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!

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

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

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0second 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?

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

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

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

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

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

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

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

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

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Don't pay attention to the left part yet!

Chlorophyll
 2 years ago
Best 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)

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1That's what Callisto has been working so hard to show you the concept!

JayDS
 2 years ago
Best 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)

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Actually 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 = ....?

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

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

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

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1I 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!

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

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

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

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

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0Maybe you can only do because you have already reached 99 smart points or something.

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1No, you can check anybody profiles!

JayDS
 2 years ago
Best ResponseYou've already chosen the best response.0yeh 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.

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