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# Core 3 Question watch

1. Can someone explain how to do ii part b please.
2. (Original post by james813)

Can someone explain how to do ii part b please.
Notice that in the (i) identity gives you the left hand side of the equation. Does this help?
3. Theta equals 1/3b+20
Solve in theta terms first using part 1
Then equate to 1/3 b +20 and solve
4. (Original post by notnek)
Notice that in the (i) identity gives you the left hand side of the equation. Does this help?
I think so, thanks.
So you can substitute it into the answer from part i and solve for beta?
5. (Original post by james813)
I think so, thanks.
So you can substitute it into the answer from part i and solve for beta?
Yes.
6. How do you do ii part a?
7. (Original post by geohan)
How do you do ii part a?
Note the question wording, it says details of transformation and this most likely means describing in words.

It would be helpful if you compare y = R sin(theta + alpha) to

yB = K x f(x+a).

Similar to yB's tranformation to f(x), you can say shift left by alpha (this is called phase shift). So, phase shift left by alpha radiants.

Then, enlarge (1/ R) (if R < 1) or shrink by (1/R) (if R > 1) about theta axis.

R = (square root of 61 ) / 2

So, in this case, shrink y values by (2 / (square root of 61 )) factor about theta axis.

I think this is what the examiner is expecting.

On the otherhand, you might be expected express transformation in algebraic form where possible, like
f(x+a) = f(x) - a
8. (Original post by geohan)
How do you do ii part a?
Note the question wording, it says details of transformation and this most likely means describing in words.

It would be helpful if you compare y = R sin(theta + alpha) to

yB = K x f(x+a).

Similar to yB's tranformation to f(x), you can say shift left by alpha (this is called phase shift). So, phase shift left by alpha radiants.

Then, enlarge (1/ R) (if R < 1) or shrink by (1/R) (if R > 1) about theta axis.

R = (square root of 61 ) / 2

So, in this case, shrink y values by (2 / (square root of 61 )) factor about theta axis.

I think this is what the examiner is expecting.

On the otherhand, you might be expected express transformation in algebraic form where possible, like
f(x+a) = f(x) - a
9. Alternatively you could expand the cos(theta - 60) using double angle formulae, then simplify using values for cos(60), etc.
10. (Original post by TIF141)
Alternatively you could expand the cos(theta - 60) using double angle formulae, then simplify using values for cos(60), etc.
If you mean it for (i), then that's fine.

Very carefully read the question, the emphasis is on the word "Hence".

So, you are expected to use the previous results and answering the question is a form of mathematical deduction process (like induction process).

Therefore, I think expanding will not accepted by examiner.

If the wording is "Hence or otherwise", then it is reasonable to use cos (A+B) expansion.

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