M. I.
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Hiya, I'm studying for an upcoming trig examn and im a bit stuck on one of the example problems, could anyone maybe walk me through it. Thank you

The height of tide at the entrance to a harbour on a particular day can be modelled by the function h=3+2sin30t+1.5cos30t, where h is measured in meters, t in hours after midnight and 30t is in degrees.
(The values 2 and 1.5 represent the relative effects of the moon and sun respectively)

I. Show that 2sin30t+1.5cos30t can be written in the form 2.5sin(30t+a), where a is to be determined.
Ii. Find the height of tide at high water and the first time this occurs after midnight.
Iii. Find the range of the tide during the day.
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RDKGames
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(Original post by M. I.)
Hiya, I'm studying for an upcoming trig examn and im a bit stuck on one of the example problems, could anyone maybe walk me through it. Thank you

The height of tide at the entrance to a harbour on a particular day can be modelled by the function h=3+2sin30t+1.5cos30t, where h is measured in meters, t in hours after midnight and 30t is in degrees.
(The values 2 and 1.5 represent the relative effects of the moon and sun respectively)

I. Show that 2sin30t+1.5cos30t can be written in the form 2.5sin(30t+a), where a is to be determined.
Ii. Find the height of tide at high water and the first time this occurs after midnight.
Iii. Find the range of the tide during the day.
What's confusing, exactly?
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M. I.
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(Original post by RDKGames)
What's confusing, exactly?
See I think its because of how the answer has to be structured, like the first part I feel pretty ok with but part ii and iii are what have me confused on where to begin and what to do from there.
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RDKGames
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(Original post by M. I.)
See I think its because of how the answer has to be structured, like the first part I feel pretty ok with but part ii and iii are what have me confused on where to begin and what to do from there.
For (ii) I can only assume they want to figure out the first instance when the tides are at their highest point. So, use your answer to part (ii) to first figure out what the greatest height if a tide can be and under what condition on \sin(30t+a) this occurs. Use the condition to determine the smallest value of t \geq 0 for which the condition is satisfied.

(iii) is simply looking for how spread apart the greatest and least possible heights of the tides are.
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