Question

Which of the following is a sinusoid? (attached below)

Please explain. Thank you!

Answer 1

what do you think sinusoid means?

Answer 2

isn't that a curve

Answer 3

yeah, a periodic curve

Answer 4

http://mathworld.wolfram.com/Sinusoid.html

Answer 5

I'll check that out

Answer 6

I always thought of sin as sinusoid , but could cosine also be considered sinusoidal function?

Answer 7

since cosine is just sine shifted out of phase

Answer 8

b. doesent have a curve so that is out right?

Answer 9

Im not sure what those bra-kets are for, maybe absolute value, but yeah it is out, linear style function

Answer 10

c. is just a circle

Answer 11

right, that is the unit circle, centered at the origin and radius 1

Answer 12

that would just leave me with a and d

Answer 13

do you remember what root functions look like?

Answer 14

a function expressed by x1/n for positive integer n greater than 1

Answer 15

those are increasing roots of x

Answer 16

and a y=sin x looks like this

Answer 17

yes, if you use desmos graph online, you can do this ....

Answer 18

see the sliders for a,b,c,d on there?

Answer 19

ok I will check out desmos

Answer 20

you can change the amplitude, period, vertical and horizontal shifts, by sliding those bars

Answer 21

put in that equation Asin(bx+c)+d

Answer 22

but yeah, sinusioid means like a curve similar to sin(x), but it can have all that extra stuff in it, the a,b,c,d terms like i added
It is a more general term sinusoid for the trig function sine

Answer 23

oh ok so y=sin x is a sinusoid

Answer 24

correct, even the name sounds similar

Answer 25

sine is the function, sinusoid is a word to describe the pattern

Answer 26

sinusoidal

Answer 27

oh ok so we eliminated b. and c. I don't even know what d. is but y=sin x = sinusoid I understand it better. Thanks!