Hello , how come this works? (trig question)

Sketch the graph of y = sin x and consider the symmetry?

Reply 2

joostan

Original post by laurawoods

Hello , how come sin(-pi*b) can be written as -sin(pi*b). I thought we couldn't move around things inside the brackets of trig functions? pls help ? thanks for any help in advance!

Normally you can't, you're right.
A general point:

\ sin(-x) = -sin(x)

Think about the graph :smile:

Also

\ cos(x) = cos(-x)

(edited 11 years ago)

Reply 3

Original post by Mr M

Sketch the graph of y = sin x and consider the symmetry?

It would be reflected in the line y axis right?

Reply 4

Original post by laurawoods

It would be reflected in the line y axis right?

That is the graph of

y = \sin |x|

so no. Could you draw it from -360 degrees to 360 degrees and it will answer your question?

Reply 5

Original post by Mr M

That is the graph of

y = \sin |x|

so no. Could you draw it from -360 degrees to 360 degrees and it will answer your question?

Hello, yes what I did is I drew, the graph of sinx , then drew the other two sin(-x) and -sin(x). The latter two are the same , isn't it ? But what I was wondering is: are we meant to know this or not? It seems obvious that they are the same when the graph is constructed, but otherwise how are we meant to know this simply by looking at it? Because one of the question I saw in a paper required the use of this knowldeg/

Reply 6

Original post by laurawoods

There are two rules you ought to learn.

\cos (-x) = \cos(x)

because cos is an even function

\sin (-x) = - \sin (x)

because sin is an odd function

http://www.mathsisfun.com/algebra/functions-odd-even.html

Reply 7

Original post by Mr M

There are two rules you ought to learn.

\cos (-x) = \cos(x)

because cos is an even function

\sin (-x) = - \sin (x)

because sin is an odd function

http://www.mathsisfun.com/algebra/functions-odd-even.html

hello ! does odd and even functions come under edexcel too? because i don't remember learning them at all?

Reply 8

bananarama2

Original post by laurawoods

hello ! does odd and even functions come under edexcel too? because i don't remember learning them at all?

Whilst the terms odd and even aren't explicitly used I think those two examples are required for edexcel.

Reply 9

Original post by laurawoods

hello ! does odd and even functions come under edexcel too? because i don't remember learning them at all?

It is just general mathematical knowledge. I have no idea whether Edexcel would expect you to be aware of them but it isn't hard and you have seen them now.

Reply 10

Robbie242

Original post by laurawoods

hello ! does odd and even functions come under edexcel too? because i don't remember learning them at all?

It comes up in C2 edexcel so I suspect its a prerequisite from AS level knowledge

Reply 11

Original post by Mr M

It is just general mathematical knowledge. I have no idea whether Edexcel would expect you to be aware of them but it isn't hard and you have seen them now.

cool thanks!

Reply 12

Hasufel

another way to look at this also is, it might also help to see this if you use the formula for

Sin(A+B)

to expand:

Sin(-x) \equiv Sin(\pi-(x+\pi))

sin(\pi)cos(x+\pi)-cos(\pi)sin(x+\pi)

0-(-sin(x+\pi))

sin(x)cos(\pi)+cos(x)sin(\pi)

sin(x)(-1)=-sin(x)

Reply 13