WEBVTT
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The depth of the water in a fishing port is usually 28 meters.
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The tidal movement is represented by π equals four times sin of 15π degrees plus 28, where π is the time elapsed in hours after midnight.
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How many times a day is the depth of the water 24 meters?
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Weβre given a function that models the movement of the water.
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And that is, π equals four times sin of 15π degrees plus 28.
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It would be helpful to first establish the parameters for π, what π can be.
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Weβre wondering how many times a day the depth of the water is 24 meters.
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And so, weβre dealing with one day, 24 hours.
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And if our π is the time elapsed in hours, then we can have an π variable that is greater than or equal to zero or less than or equal to 24.
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We can use this information to find out what 15π degrees must then be.
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15 times zero would be zero degrees.
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15 times 24 is 360 degrees.
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And so, we can say that weβre dealing with sine functions of one rotation, from zero degrees to 360 degrees.
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If we think about sketching a sine function, we take a range of π₯ values from zero to 360 degrees.
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Sin of zero degrees is zero.
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We know that sin of 90 degrees is one.
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Sin of 180 degrees is zero.
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Sin of 270 degrees is negative one.
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And sin of 360 degrees is also zero.
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This is the graph of π¦ equals the sin of π₯ degrees.
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If we wanted π¦ equals four times the sin of π₯ degrees, well sin of zero degrees times four is still zero.
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Sin of 90 degrees is one, and one times four is four.
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Four times the sin of 180 degrees is still zero, as would be four times the sin of 360 degrees.
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Four times the sin of 270 degrees would be equal to negative four.
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It would be four times negative one.
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So, we see the way multiplying four by the sine function stretches it in the vertical direction.
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And now, we need to deal with this 28 meters.
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We know that the water is regularly at 28 meters.
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When the water starts at 28 meters and makes an increase of four meters, itβs at 32 meters.
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And when the water makes a decrease of four meters, itβs set at 24 meters.
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Based on this model, the tide only goes down to 24 meters one time in a 24-hour period.
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The question was not asking what time of day the tide hits 24 meters, but how many times a day.
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And based on this information, it only happens one time.