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# FP2 loci question (edexcel) watch

1. Hi!

I came across this question in my book and as you can see in the first attached pic I was only able to find one half-line (pi/3).

According to the book there are two half-lines (pic 2).

Can anyone tell me where the second one (-2pi/3) comes from?

Any help would be greatly appreciated
Attached Images

2. (Original post by WatermelonJuice1)
Hi!

I came across this question in my book and as you can see in the first attached pic I was only able to find one half-line (pi/3).

According to the book there are two half-lines (pic 2).

Can anyone tell me where the second one (-2pi/3) comes from?

Any help would be greatly appreciated
tanθ = √ 3

has solutions in a full circle
θ = π/3
θ =4 π/3 = -2 π/3

does this help?
3. (Original post by TeeEm)
tanθ = √ 3

has solutions in a full circle
θ = π/3
θ =4 π/3 = -2 π/3

does this help?
It did help, but in the previous question they only wanted the half-line given by the first result which confused me.
4. (Original post by WatermelonJuice1)
It did help, but in the previous question they only wanted the half-line given by the first result which confused me.
I know nothing about the previous question
questions are different.
5. (Original post by TeeEm)
I know nothing about the previous question
questions are different.
The previous Q (part a of the same question) was the following:

arg(z)=arctan(2)

arctan(2)=63.4 , 243.4

Both can be represented on an Argand diagram but in the back of the book, only the first one is.

Am I always expected to find both? Would this be specified in an exam? Thanks.
6. (Original post by WatermelonJuice1)
The previous Q (part a of the same question) was the following:

arg(z)=arctan(2)

arctan(2)=63.4 , 243.4

Both can be represented on an Argand diagram but in the back of the book, only the first one is.

Am I always expected to find both? Would this be specified in an exam? Thanks.
the arctan2 = 63.4 and NOT 243.4

the statement tanθ = 2 and arctan2 = θ are NOT equivalent as the tan is NOT a one to one function

a simple analogy

x2=4 and x = √4 are not euivalnent
7. (Original post by TeeEm)
the arctan2 = 63.4 and NOT 243.4

the statement tanθ = 2 and arctan2 = θ are NOT equivalent as the tan is NOT a one to one function

a simple analogy

x2=4 and x = √4 are not euivalnent
Ok, I get it now. Thanks a lot.

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