# Cambridge Maths Interview QuestionWatch

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#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?
0
4 years ago
#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?
0
#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..
0
4 years ago
#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.
1
4 years ago
#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 .

1
4 years ago
#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.
0
4 years ago
#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.
0
4 years ago
#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".
0
#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?
0
4 years ago
#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.
0
3 weeks ago
#11
Looking at this question, I think the quickest way is that, if you are familar with the transformation of tan(x/2), the relationship is such that sin2x=2t/(1+t2),cos2x=(1-t2)/(1+t2), and the question reduces to (t-1)(t+1)2=0. Where t is tanx.
0
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