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# Cambridge Maths Interview Question watch

1. if theta represents an angle such that sin2theta= tan theta - cos2theta,
then sintheta - costheta = ?

A - root2
B 0
C 1
D 2 root 2
E It cannot be determined

Yes you can put it into an equation solver and get the right answer.

But may I ask how you did it?
2. (Original post by Damien_Dalgaard)
if theta represents an angle such that sin2theta= tan theta - cos2theta,
then sintheta - costheta = ?

A - root2
B 0
C 1
D 2 root 2
E It cannot be determined

Yes you can put it into an equation solver and get the right answer.

But may I ask how you did it?
3. (Original post by ThatPerson)
I thought that too by Newton Raphson but the answer is apparently - root 2. Plugged it in to my casio fx991es not sure why though..
4. (Original post by Damien_Dalgaard)
I thought that too by Newton Raphson but the answer is apparently - root 2. Plugged it in to my casio fx991es not sure why though..
Ah, I see it now. There is more than one solution because x can take multiple values.

Spoiler:
Show

After some rearranging and using we arrive at

or

The latter results in 0, whilst the former produces . Hence the solution to cannot be determined.
5. (Original post by ThatPerson)
Ah, I see it now. There is more than one solution because x can take multiple values.

Spoiler:
Show

After some rearranging and using we arrive at

or

The latter results in 0, whilst the former produces . Hence the solution to cannot be determined.
I did it in a different way but got the same answers, not sure why is undetermined.

Let and

Then

So meaning

And if then .

For then .

6. (Original post by Gawain)
I did it in a different way but got the same answers, not sure why is undetermined.

Let and

Then

So meaning

For then .

Your answer also shows that it is undetermined. If there are two possible answers then you can't say the solution to (sinx - cosx) is either one, despite one of the possible answers being an option.
7. (Original post by ThatPerson)
Your answer also shows that it is undetermined. If there are two possible answers then you can't say the solution to (sinx - cosx) is either one, despite one of the possible answers being an option.
Since A and B are both true I guess it has to be the last one, but the answer didn't say 'undetermined' (i.e. needs a suitable domain for a singular answer) but rather 'cannot be determined'.

I took issue with the word 'cannot' because it clearly can be determined if given a suitable domain.
8. (Original post by Gawain)
Since A and B are both true I guess it has to be the last one, but the answer didn't say 'undetermined' (i.e. needs a suitable domain for a singular answer) but rather 'cannot be determined'.

I took issue with the word 'cannot' because it clearly can be determined if given a suitable domain.
I view the two phrases as synonymous, and I think it's implied in both that the answer cannot be determined in an unrestricted domain.

I think this is more an issue of semantics rather than the actual answer, and additionally the last option also uses the phrase "cannot be determined".
9. (Original post by ThatPerson)
Ah, I see it now. There is more than one solution because x can take multiple values.

Spoiler:
Show

After some rearranging and using we arrive at

or

The latter results in 0, whilst the former produces . Hence the solution to cannot be determined.
(Original post by Gawain)
I did it in a different way but got the same answers, not sure why is undetermined.

Let and

Then

So meaning

And if then .

For then .

Good methods, I kind of made a mess in doing in similar to @Gawain
Probably should have got that though.

So have you guys unanimously decided that its E.

With respect to the unrestricted domain, I suppose that would be considered too. I was was just quoting it as it was written?
10. (Original post by Damien_Dalgaard)
Good methods, I kind of made a mess in doing in similar to @Gawain
Probably should have got that though.

So have you guys unanimously decided that its E.

With respect to the unrestricted domain, I suppose that would be considered too. I was was just quoting it as it was written?
I'm confident it's E.

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