How do I graph a horizontal compression with trig functions?

[CrossFit415]

Homework Statement

Y = - sin (2X)

Homework Equations

The Attempt at a Solution

So.. I know how to graph - sin, that's going to be one 1 but reversed. Now my problem is the (2x). How do I graph 2x in the trig graph? How would I go about making a horizontal compression? Thank you

 

[tiny-tim]

Hi CrossFit415!

Find all the points where sin2x = 0 …

that's where the graph has to cross the x-axis.

 

[CrossFit415]

Thanks Tim

 

[LCKurtz]

Homework Statement

Y = - sin (2X)

Homework Equations

The Attempt at a Solution

So.. I know how to graph - sin, that's going to be one 1 but reversed. Now my problem is the (2x). How do I graph 2x in the trig graph? How would I go about making a horizontal compression? Thank you

Tim has given you one method. Another is to just draw a sine curve on an unlabeled axis. Using the fact that the period of sin(bx) is 2pi/b you know the period of your function is pi. So mark x = pi at the end of the first period and label everything else accordingly.

 

[CrossFit415]

Tim has given you one method. Another is to just draw a sine curve on an unlabeled axis. Using the fact that the period of sin(bx) is 2pi/b you know the period of your function is pi. So mark x = pi at the end of the first period and label everything else accordingly.

Ok, so if I wanted to graph sin (1/2)x I would solve for 2 pi / (1/2) = 4pi. So how would I draw my graph compared to sin x?

 

[Mentallic]

Ok, so if I wanted to graph sin (1/2)x I would solve for 2 pi / (1/2) = 4pi. So how would I draw my graph compared to sin x?

sin(x) has a period of $2\pi$ (that is, it repeats itself every $2\pi$) and since sin(x/2) has a period of $4\pi$ it would look...?

 

[LCKurtz]

Ok, so if I wanted to graph sin (1/2)x I would solve for 2 pi / (1/2) = 4pi. So how would I draw my graph compared to sin x?

So label the end of the first period 4pi and everything else accordingly.