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Trig: graphs and equations question

I am confused at this question:

The minimum depth, d ft, of water in a harbor t hours after midnight can be approximated by the function
d(t)=35+15cos0.5twhere0≤t≤24\qquad\qquad d(t) = 35 + 15cos0.5t \quad where \quad 0 \leq t \leq 24
A ship with a draught of 25 ft is in harbor at midnight. By what time must it leave to prevent grounding?

I don't understand what draught exactly means, even after googling. Seeing there was a value, I set d(t) = 25 and solved for t:

35+15cost0.5t=2535 + 15cost0.5t = 25
15cost0.5t=−1015cost0.5t = -10
0.5t=cost−1(−10/15)0.5t = cost^{-1}(-10/15)
t=263.620...t=263.620...

The answer is 4.36am. I've tried sketch a graph and looking at it but it makes no sense. I need a few pointers please!
Original post by tenki
I am confused at this question:

The minimum depth, d ft, of water in a harbor t hours after midnight can be approximated by the function
d(t)=35+15cos0.5twhere0≤t≤24\qquad\qquad d(t) = 35 + 15cos0.5t \quad where \quad 0 \leq t \leq 24
A ship with a draught of 25 ft is in harbor at midnight. By what time must it leave to prevent grounding?

I don't understand what draught exactly means, even after googling. Seeing there was a value, I set d(t) = 25 and solved for t:

35+15cost0.5t=2535 + 15cost0.5t = 25
15cost0.5t=−1015cost0.5t = -10
0.5t=cost−1(−10/15)0.5t = cost^{-1}(-10/15)
t=263.620...t=263.620...

The answer is 4.36am. I've tried sketch a graph and looking at it but it makes no sense. I need a few pointers please!

Are you working in radians?
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Avatar for tenki
tenki
OP
Original post by keromedic
Are you working in radians?


No, why do you ask?
Original post by tenki
No, why do you ask?


You should be.

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