Trigonometric identities

Determine a sequence of transformations which maps the graph of y=sinx onto the graph of y=(root3) sinx-3cosx+4

Study Forum Helper

Original post by 01sbrals

Determine a sequence of transformations which maps the graph of y=sinx onto the graph of y=(root3) sinx-3cosx+4

Express the transformed graph in the form

R\sin(x+\alpha) + A

then its obvious.

OP

Original post by RDKGames

Express the transformed graph in the form

R\sin(x+\alpha) + A

then its obvious.

I worked it out to be 2root3 sin (x-30). what would i do after that?

Study Forum Helper

Original post by 01sbrals

I worked it out to be 2root3 sin (x-30). what would i do after that?

What happened to the +4 ?

OP

Original post by RDKGames

What happened to the +4 ?

2root3 sin (x-30) +4
sorry

Study Forum Helper

Original post by 01sbrals

2root3 sin (x-30) +4
sorry

I'm just going to assume it's correct.

So then rearrange into

\dfrac{y-4}{2\sqrt{3}} = \sin(x-30)

.

What transformations have taken place to get from

y=\sin x

??

Hint: there is one horizontal transformation, and two vertical ones.

OP

Original post by RDKGames

I'm just going to assume it's correct.

So then rearrange into

\dfrac{y-4}{2\sqrt{3}} = \sin(x-30)

.

What transformations have taken place to get from

y=\sin x

??

Hint: there is one horizontal transformation, and two vertical ones.

vertical stretch by 2root 3
translation by 30 to the right
and translation 4 up?

Study Forum Helper

Original post by 01sbrals

vertical stretch by 2root 3
translation by 30 to the right
and translation 4 up?

Thats right.

Always remember to write the order of transformations when talking about two or more transformations happening along one axis.

For instance, you are correct if we stretch vertically first before applying the translation, but if we do the translation first and then the stretch then the magnitudes of these are not necessarily the same.

I think it’s wrong no, the translation is correct but shouldn’t it be 60 instead of 30Tan^-1 of sqrt3/3 =60? Its tan^-1B/a = alpha

(edited 2 months ago)

I think it’s wrong no, the translation is correct but shouldn’t it be 60 instead of 30Tan^-1 of sqrt3/3 =60? Its B/a = alpha

Quick Reply

Latest

Trending

Trending

Articles for you

The Student Room Group Privacy Notice

FAQ: how The Student Room treats your data

FAQ: how The Student Room treats your data

Dependants’ Grants - How to Apply

General forum usage