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maths a level trigonometric identities

i don't know how to approach this question.. should i start by using double angle formulae? but i don't understand how that would help me figure out what the transformations are.
1.JPG
(edited 2 years ago)
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Avatar for mqb2766
mqb2766
21
Original post by abovethecl0uds
i don't know how to approach this question.. should i start by using double angle formulae? but i don't understand how that would help me figure out what the transformations are.
1.JPG

The double angle expression can be put in terms of a single trig term like
Asin(2x + alpha)
So ...
Original post by mqb2766
The double angle expression can be put in terms of a single trig term like
Asin(2x + alpha)
So ...

I got:
stretch of scale factor 0.5 parallel to the x axis
stretch of scale factor 5 parallel to the y axis
translation of 0.927 3sf radians in the negative x direction
Original post by abovethecl0uds
I got:
stretch of scale factor 0.5 parallel to the x axis
stretch of scale factor 5 parallel to the y axis
translation of 0.927 3sf radians in the negative x direction

Care needed here. If you apply the first two transformations, you get 5sin(2x). So far so good. But what happens to that when you replace x by (x + 0.927)?
Original post by old_engineer
Care needed here. If you apply the first two transformations, you get 5sin(2x). So far so good. But what happens to that when you replace x by (x + 0.927)?

Isn't that a translation by 0.927 parallel to the x axis in the negative direction?
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mqb2766
21
Original post by abovethecl0uds
Isn't that a translation by 0.927 parallel to the x axis in the negative direction?

Its sometimes easier if you introduce a temporrary variable z so
sin(z)
where
z = 2x + 0.9
So
x = (z-0.9)/2 = z/2 - 0.45
The last two expressions are obviusly equivalent but the transformations are different. Yours is the latter? Importantly, the order of the transformations is different, so the scaling affects the translation
(edited 2 years ago)
Original post by mqb2766
Its sometimes easier if you introduce a temporrary variable z so
sin(z)
where
z = 2x + 0.9
So
x = (z-0.9)/2 = z/2 - 0.45
The last two expressions are obviusly equivalent but the transformations are different. Yours is the latter? Importantly, the order of the transformations is different, so the scaling affects the translation

Ok so the order is: horizontal translation first, then stretching
Thanks always for your help :smile:
Reply 7
Avatar for mqb2766
mqb2766
21
Original post by abovethecl0uds
Ok so the order is: horizontal translation first, then stretching
Thanks always for your help :smile:

Or you stretch first then translate by 1/2 the value in this case.
You can do either, but not what you originally said.
(edited 2 years ago)

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