SOLUTION: Hi can someone help me with this problem please? THANK YOU! At 3:00 p.m. one summer day,the wave height off the coast of harbourtown could be modeled with the equation y=3.3

Algebra ->  Trigonometry-basics -> SOLUTION: Hi can someone help me with this problem please? THANK YOU! At 3:00 p.m. one summer day,the wave height off the coast of harbourtown could be modeled with the equation y=3.3      Log On


   

Question 1077469: Hi can someone help me with this problem please? THANK YOU!
At 3:00 p.m. one summer day,the wave height off the coast of harbourtown could be modeled with the equation y=3.3(2pi/7 t)+0.2,where t is measured in seconds and y in feet.Use the model to find the wave height from peak to trough.
Select One:
a. 3.3ft
b. 0.2ft
c. 0.4ft
d. 6.6ft
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There is a typo in this problem.
If y=3.3%28%282pi%2F7%29t%29 , y would increase with time without limit.

It should be
y=3.3cos%28%282pi%2F7%29t%29%2B0.2=3.3cos%282pi%2At%2F7%29%2B0.2 or
y=3.3sin%28%282pi%2F7%29t%29%2B0.2=3.3sin%282pi%2At%2F7%29%2B0.2 .
(Waves use a cosine or sine trigonometric function term).
That way you would have an average height of 0.2 ft,
but height oscillates between times where
cos%28%282pi%2F7%29t%29=-1 (or cos%28%282pi%2F7%29t%29=-1 depending on how the function is written),
and times where the same trigonometric function's value is 1 .
Since the trigonometric function is multiplied times 3.3 ,
that term would oscillate between -3.3 and 3.3 ,
a difference of 3.3-%28-3.3%29=highlight%286.6%29 .