C3 Transformations Maths Question - HELP

I am currently revising transformations and seem to be getting confused.
Every question I encounter I use these rules;

y = f(x-a) + b ----> Translation [a, b]
y = f( -x) ------> Reflection in y-axis
y = - f(x) -----> Reflection in x-axis
y = f ( x/a) -----> Stretch in x-axis by a
y = a f (x) ---> Stretch in y-axis by a

I sometimes bring everything affecting the y to the other side and that makes it easier.
Anyways the question I don't understand is....;

"Describe geometrically how the curve y = 1 + sinx is transformed into y = 1 - sinx" - The answer at the back of the book is reflection in y-axis.

When I do it;
y = 1 - sinx
y - 1 = -sinx
-(y -1) = sinx >> Reflection in x-axis??
I don't understand how it is a reflection in the y-axis?
Does anyone have any techniques to approaching a question - I need to nail ANY transformation question

HELP

are you from abroad or the UK?

I am currently revising transformations and seem to be getting confused.
Every question I encounter I use these rules;

y = f(x-a) + b ----> Translation [a, b]
y = f( -x) ------> Reflection in y-axis
y = - f(x) -----> Reflection in x-axis
y = f ( x/a) -----> Stretch in x-axis by a
y = a f (x) ---> Stretch in y-axis by a

I sometimes bring everything affecting the y to the other side and that makes it easier.
Anyways the question I don't understand is....;

"Describe geometrically how the curve y = 1 + sinx is transformed into y = 1 - sinx" - The answer at the back of the book is reflection in y-axis.

When I do it;
y = 1 - sinx
y - 1 = -sinx
-(y -1) = sinx >> Reflection in x-axis??
I don't understand how it is a reflection in the y-axis?
Does anyone have any techniques to approaching a question - I need to nail ANY transformation question

HELP

UK, why?

This uses the fact that -sinx = sin(-x)

For this to be a reflection in the x-axis you would need y = -(1+sinx) = -1-sinx

nothing to worry
it is just the way you are attempting this, reminds me of approaches taught abroad...

Yes I've heard about that: -sinx = sin -x, is that just because it's an odd function? Does is then work with tanx as well? and when do you know to do that/or is it always?

I get what you mean with "y = -(1+sinx) = -1-sinx" so does that mean the answer in the book is wrong?

Are you from UK? Do you know any other approach that may be easier? At the minute I'm just learning it independently and trying to master transformations (since I always lose some marks in these questions) and my teacher isn't............ very "effective" shall we say?

No the book is correct

y = 1 - sinx = 1 + sin(-x) = f(-x) so a reflection in the y-axis

Ok that makes sense Thank you!!!
So is f(-x) always = -f(x) in odd functions??
Because in e.g. y = -x^2, is not the same as (-x)^2?

do not worry ... you may be too conscientious
this is genuinely a hard question.

This transformation is very hard to see.

I have 9 Year 13 students this year with varying AS UMS from 263 to 295.

practically all of them will get A* but I think NONE of them would have seen this ...

Yes, in odd functions - not in even functions

It's reassuring to know it's a difficult question, I am aiming for an A* so I want to nail any transformation question I can find but this one put me off...
At the minute I am thinking (thanks to TenOfThem) that I have to use what he/she suggested -f(x) = f(-x) but then if I use that in other questions I find it doesn't always work - don't know if it's just me that's doing the question wrong (I figured it only works with odd functions - so do I just use it for odd functions).

unfortunately this is true (use of odd functions)

but I have never seen a question like this in any recent exam.

I'm doing AQA and there's none like these in past papers either but there is in the textbook so I think my best bet is to try to understand it in case (you never know what they're going to throw at you the next year)

I do not think Odd/even functions are taught at current AQA syllabus, but it does not hurt to know...

Oh ok, so do I not need to know about that transformation in AQA (odd and even functions)?

I last time I taught AQA students were in 2011 - 2013 and that was not part of their course.
I do not think the Syllabus has changed.

only board that does this topic, at standard A level, is MEI

Ok thank you for the info, I think I'm going to just leave it, I understand it-ish at least.
Can I ask another question, cosecx --> cosec(2x +30)
I would do cosec(2(x +15)), does it matter which way round it is?
stretch in x-direction by 1/2 and translation [-15, 0]
OR
translation [-30, 0] and stretch in x-direction by 1/2

Are they both correct???