#Anyone know where I can find more questions that are specifically like this? With the unknown angle

115 messages · Page 1 of 1 (latest)

charred craneBOT
sage canyon
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most questions like this are not going to be repeated
theyre more like unique puzzles where you need to figure out whats happening and then solve for it

rare meadow
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ive solved 4 alike

sage canyon
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the question is asking you what angles dont face towards the circle

rare meadow
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so they arent that unique

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same procedure each time

sage canyon
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then do the same method as those previous 4

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whats stopping you

rare meadow
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I am asking for MORE questions like that

sage canyon
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you already have enough

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these are too tedious

rare meadow
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I mean I will be the judge of that lmao

sage canyon
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if I just give you a random circle, do you really want to do more of the same thing?

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youre not a robot

rare meadow
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yeah I do want to do the same thing

sage canyon
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then you look at this and you tell me how much you like it:

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find the range of values for θ, -π < θ ≤ π, for which arg(z) = θ and one of the following equations below have no common solutions:

  1. |z + 1| = 0.5
  2. |z + 9| = 2
  3. |z + 8i| = 3
  4. |z + 7| = 4
  5. |z - 6i| = 5
  6. |z + 6| = 5.1
  7. |z + 6| = 5.11
  8. |z + 6| = 5.12
  9. |z + 9999 + 9998i| = 9997
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alternatively you can do |z + a| = b

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figure that out

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and solve every possible problem with one formula

sage canyon
rare meadow
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Okay can u explain this tho

sage canyon
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no

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you have 9 problems to do

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you be the judge of how you best use your time

rare meadow
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its not about those questions its about the first image I sent

sage canyon
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would doing 9 problems answer it

rare meadow
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no

sage canyon
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then you can see how pointless it is to do any of them

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they dont help you figure anything out

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they just get a method down

rare meadow
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it will help me answer the other 9 probelms and understand the topic very well all around though

sage canyon
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theres already a direct formula for these, you dont need to do problems that explain nothing all day

sage canyon
atomic hazel
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i think

sage canyon
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notice youre still not typing your question

atomic hazel
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both of you have a different pov

sage canyon
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we'll be the judge of that when I even get to see b's original question

atomic hazel
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see

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i think what b's trying to ask is

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they need help w these particular types of questions

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and

sage canyon
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doing the same problem does not answer conceptual questions

atomic hazel
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once they get the hang of it

atomic hazel
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and i agree

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but

sage canyon
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they already did 4 of them

atomic hazel
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let them figure that out themselves

sage canyon
atomic hazel
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sometimes

rare meadow
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the thing is the probelms u sent are much easier

sage canyon
atomic hazel
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some people learn from doing it on their own

sage canyon
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go do them

rare meadow
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because the angle is always about the origin

atomic hazel
rare meadow
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yeah

atomic hazel
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i think thats how these always are tbh

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which board are you doing

sage canyon
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all the z - (4 - 2i) does here is shift the z somewhere else before measuring the angle

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you can counteract this by replacing every mention of z in the problem withz + 4 - 2i

atomic hazel
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yeah

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i think theyre all like this

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j get the hang of it

sage canyon
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by doing this, you reduce the problem down to one you already know

atomic hazel
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and if youve done 4

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i think youre good to go

sage canyon
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youve already done to many, but youve done them all

atomic hazel
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it would j be a waste of time

sage canyon
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I called these puzzles earlier

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the solution to figuring out puzzles isnt to do more of them if your method of solving them is to look up the answer and follow it to a T

sage canyon
rare meadow
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good for u man

sage canyon
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Im the one figuring these out for you man

rare meadow
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yeah ur not

sage canyon
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in case its not clear, you are trying to solve:

  • arg(z - 4 + 2i) = θ
  • |z + 6 + 6i| = 4
    which you can make easier by replacing z with z + 4 - 2i to get:
  • arg(z) = θ
  • |z + 10 + 4i| = 4
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then its similar to the 9 questions that you already know a method to solving

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if you just want the practice the method, I want to warn you that thats not what math is about at all, but you can go do that

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that will be your final warning

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you can go ahead and do those problems then

sage canyon
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you should figure that one out first before asking for more

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do things one step at a time

sage canyon
# sage canyon if you want problems that hide the answer in different ways, you still havent do...

but if youre really going to skip ahead of your question, heres a couple more questions that hide the same method in different ways:

  1. find the range of values for θ, where -2 < θ ≤ -2 + 2π, for which arg(z) = θ and |z + 4 + 10i| = 3
  2. find the range of values for θ, where -π < θ ≤ π, where arg(z) = θ shares no solutions with |z + 2i| = 1 nor |z - 2| = 1
  3. find the range of values for θ, where -π < θ ≤ π, where arg(z) = θ shares a solution with |z - 3i| = 2
  4. find the range of values for θ, where -π < θ ≤ π, where arg(z) = θ shares a solution with |z| = 1
  5. find the range of values for θ where arg(z - 4 + 2i) = θ and |z + 6 + 6i| = 4 (this is tricky, I left out information here that would usually be assumed - your range is harder than it looks)
  6. find the range of values for θ, where arg(z) = θ and is a solution to only and exactly one of the two inequalities |z - 3 - 3i| < 4 and |z - 3 + 3i| < 4
  • find the range of values for z where arg(z) = π/2 and |z - 4 - 3i| ≤ 4.5 (whoops this one uses a different method but you said you were good with this stuff so I think youll be able to figure this one out)
sage canyon
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you look at this answer and you tell me that says "I want questions that actively hide the method" instead of "I want questions of only the exact same method"

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with that out of the way,

sage canyon
sage canyon
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do you get how to do the 9 problems earlier?

rare meadow
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yes they are easy I am just confused how to find the range the question I sent wants

sage canyon
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I told you that earlier as well

rare meadow
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I know how to find the angle, and I get its the angles outside that angle

sage canyon
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Ill go include a question for being inside the angle then

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also @rare meadow you should know I edited question 1 so that the catch in that question applies

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its now |z + 4 + 10i|

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in case its not clear, you can make solving this easier:

  • arg(z - 4 + 2i) = θ
  • |z + 6 + 6i| = 4
    by replacing z with z + 4 - 2i to get:
  • arg(z) = θ
  • |z + 10 + 4i| = 4
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the reason you get to do this is that the question really asks for θ instead of z

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so the exact positions where z works doesnt really apply

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you also get to substitude anything in for z, as long as its the same value all around

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so if that value happens to be z + 4 - 2i, its still valid to do so

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this was chosen to change the arg(z - ...) to just be arg(z) so that its a problem you can recognize

sage canyon
# sage canyon but if youre really going to skip ahead of your question, heres a couple more qu...

these questions do some basic obfuscation to hide the method, but they always keep clear what is visually happening
arg(z - 4 + 2i) = θ does not do that, you have to read it as arg(z - (4 - (4 - 2i)) = θ to see that θ is the angle measured from (4, -2) instead of the origin

unfortunately Im not good enough at coming up with questions like those, but given you got stuck on that one I think these 6 should be enough for you to figure out on your own

sage canyon
rare meadow
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how do u do the first one? geometrically? I thought one of the ranges would be theta > -2.577

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if u could show on on a diagram it would help me a lot

sage canyon
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no cheating

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the whole point is to get you to do that yourself

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otherwise these problems will lose a lot of their impact

sage canyon
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youre not used to real practice but its the practice you really need