# Trig question, check it?

G

#### Guest

##### Guest
I posted this in another thread but I'm quite worried that I made a mistake somewhere (my friend got a different answer) and since it's due in the morning and all, I'd really appreciate someone checking it for me. Allison noted that competitive swimmers do a series of dolphin kicks upon diving into the water. She thought that the legs moved sinusoidally. The independent variable is time and dependent is the height above and below the water. At what times are the swimmer's legs 5 cm above their resting position?

time(s)|height(cm)
0.7|0
0.9|15
1.1|0
1.3|-15
1.5|0
etc, I'm sure you could figure the rest out.

I figured out that the period would be 0.8 seconds, meaning there was a horizontal stretch of 1/450.

The formula I came up with:

$$\displaystyle (1/15)y=sin450(x+0.1)$$

I then substituted y for 5 and came out with:
$$\displaystyle 450(x+0.1)=19.47+360K$$
$$\displaystyle 450(x+0.1)=160.53 +360K$$

$$\displaystyle x=0.0567+0.8K$$
$$\displaystyle x=0.2567+0.8K$$
$$\displaystyle KEI$$