## jojokiw3 one year ago When graphing this equation, where do I put this part of it?

1. jojokiw3

$y = 2+3 \sin [3(x-\frac{ \pi }{ 4 })]$ What do I do with the second 3?

2. anonymous

@SoullessEyes

3. jojokiw3

@zepdrix

4. jojokiw3

So 2 is the center line, 3 is the amplitude, pi/4 is the phase angle. What's the 3 in front of the x?

5. zepdrix

Sounds right so far! :) $\large\rm y=A \sin[B(x-C)]+D$A gives us amplitude, B gives us period in this way $$\rm Period=2\pi/B$$, C is our phase shift, D moves the center line,

6. jojokiw3

Oo, what's period?

7. zepdrix

It's the amount of time it takes for the sine function to complete one full cycle. Or in this case it would maybe be more appropriate to say, the amount of x for sine to complete a full cycle, to get back to it's starting point.

8. jojokiw3

So is it like the "distance" from one high point to the next?

9. zepdrix

|dw:1444370686674:dw|

10. zepdrix

|dw:1444370742440:dw|A single period here

11. zepdrix

Yes, that's a good way to think of it!

12. zepdrix

Usually sine function starts at the mid point though, so measuring top to top might be a little weird

13. anonymous

@zepdrix when done can u help me?

14. jojokiw3

So for cosine it's maybe top to top, but sine it's mid to mid?

15. zepdrix

|dw:1444370812720:dw|This is one full period of the normal sine curve. So careful when you say mid to mid! :) We pass through the middle an extra time.

16. zepdrix

Notice that I've captured the entire shape with these red dots, One camel hump up, and one more down. Then it repeats that over and over.

17. jojokiw3

Haha oh you're right. So basically two curves, though one of the cos curves is cut in half.

18. anonymous

nvm its 11pm i gtg

19. zepdrix

ya cosine is a little weird. you're getting half a camel hump, then the entire lower one, then another half of the upper one.

20. jojokiw3

I think I get it now. :D Thanks for explaining!

21. zepdrix

yay team \c:/