# Thread: Even more trig function help

1. ## Even more trig function help

So, apparently I'm not very good at trig so I need help with another question.

The tides at silver bay range between 3m and 12m high. High occurs at 11AM each day and low tide occurs 6 hours later.
Sketch the curve that represents the height of the tides versus the time (in hours) for two cycles beginning at high tide (11am).

2. ## Re: Even more trig function help

Originally Posted by Braedong
So, apparently I'm not very good at trig so I need help with another question.

The tides at silver bay range between 3m and 12m high. High occurs at 11AM each day and low tide occurs 6 hours later.
Sketch the curve that represents the height of the tides versus the time (in hours) for two cycles beginning at high tide (11am).
I'll pick a cos graph because that has a maximum at $\displaystyle f(0)$ which coincides with the question. The generic formula for such a graph is $\displaystyle f(t) = A\cos(Bt + C) + D$ where A,B,C and D are constants to be found. In this case however $\displaystyle C=0$ since we have a maximum at the start of the graph so there is no offset.

You know that the maximum value is 12m and the minimum 3. Since a cos graph is smooth the middle is the mean of these values: $\displaystyle \dfrac{12+3}{2} = \dfrac{15}{2}$ and so $\displaystyle D = \dfrac{15}{2}$

The question had told us that $\displaystyle f(0) = 12$ and $\displaystyle f(6) = 3$

Using this information we can say that $\displaystyle f(t) = A\cos(Bt) + 7.5$. To find A and B use the two data points above

3. ## Re: Even more trig function help

I know how to calculate A but how would you calculate B in this situation?

4. ## Re: Even more trig function help

Originally Posted by Braedong
I know how to calculate A but how would you calculate B in this situation?
Simultaneous equations. You have $\displaystyle f(0) = 12$ and $\displaystyle f(6) = 3$. Alternatively if you can find A use one of your data points to find B.

5. ## Re: Even more trig function help

Originally Posted by Braedong
I know how to calculate A but how would you calculate B in this situation?
$\displaystyle B = \frac{2\pi}{T}$ , where $\displaystyle T$ is the period of the function.