SOLUTION: Please help me with the problem below: The distance y inches between a yo-yo and Susan's had at time t seconds is given by the equation y=-15cos(2(3.14)t/2.8)+15. Steven needs t

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me with the problem below: The distance y inches between a yo-yo and Susan's had at time t seconds is given by the equation y=-15cos(2(3.14)t/2.8)+15. Steven needs t      Log On


   



Question 1000137: Please help me with the problem below:
The distance y inches between a yo-yo and Susan's had at time t seconds is given by the equation y=-15cos(2(3.14)t/2.8)+15. Steven needs to take a picture when the yo-yo is 7 inches from the hand and moving away from the hand. At what times can he take the picture?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is telling you that +y+=+7+
+7+=+15%2A%28+-cos%28+6.28t%2F2.8+%29+%2B+1+%29+
+7%2F15+=++-cos%28+6.28t%2F2.8+%29+%2B+1+
+7%2F15+-+15%2F15+=+-cos%28+6.28t%2F2.8+%29+
+8%2F15+=+cos%28+6.28t%2F2.8+%29+
+8%2F15+=+.5333+
Let +6.28t%2F2.8+=+theta+
+.5333+=+cos%28+theta+%29+
Using the inverse cos function
and setting for radians
on my calculator:
+theta+=+1.00826+
+6.28t%2F2.8+=+1.00826+
+6.28t+=+2.8231+
+t+=+.4495+ sec
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The cos function ( all cos functions ) begins at +1+, then
goes to +0+ at +theta+=+pi%2F2+
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My value, +theta+=+1.00826+, is less than +pi%2F2+, so
it is on the way down from zero inches from hand to
+15+ inches from hand when cos function is zero.
When the cos is +-1+,
yo-yo is +30+ inches from hand.
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To figure out all the times that yo-yo is +7+ in from hand
and on the way down, you must add +2%2Api+ like this:
+7+=+15%2A%28+-cos%28+6.28t%2F2.8+%2B+2%2Api+%29+%2B+1+%29+
Then you must find +t+ for +2%2Api+, +4%2Api+, +6%2Api+, etc.
You will be on the way down each of those times and
+7+ in from hand
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Hope this helps