Vanessa F.

asked • 06/25/19# Application of trigonometric functions to do with a graph about high and low tides

If the trigonometric equation is y=0.9cos(pi over 12.5 multiplied by x) and the depth of the water at low tide is 0.4m what is the depth after low tide? (2.d.p)

## 2 Answers By Expert Tutors

This is a problem which requires you to understand what parts of the given expression represent depth. It turns out that x does not matter, but the 0.9 of amplitude does. With that in mind if low tide is at 0.4, then high tide must be at 0,4 + 2(0.9) = 2.2. The reasoning here is that twice the amplitude gets added to the low point to get to the high point. The question of what depth after high tide can be solved by putting in a value for x and then adding it algebraicialy to 1.3, which is the midpoint between high and low tide. We say "algebraically" because some values of the cosine will be negative. Note that the expression given was interpreted to be the variations in tide level, not the actual tide level. If the former was the case then negative values would be obtained from the expression, which is inconsistent with a low tide level of 0.4, which is positive.

y=.9cos(3.14x/12.5)

low tide=.4m

What does "x" represent?

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Mark M.

How much time after low tide?06/27/19