what don't you get? You have the equation for d(t). Just do the math. For the graph, see
http://www.wolframalpha.com/input/?i=40%2B60cos%28%28pi%2F2%29%28t-2%29%29
For the rest, just solve for t under the given conditions:
(b) 40+60cos(PI/2(t-2)) = 76
(c) is d(t) on its way up, or down?
(d) 40+60cos(PI/2(t-2)) < 0
At a certain point on the beach, a post sticks out of the sand, it's top being 76 cm above the beach. The depth of the water at the post varies sinusoidally with time due to the motion of the tides. The depth d is modeled by the equation d=40+60cos(PI/2(t-2)) where t is the time in hours since midnight.
a. Sketch a graph of the sinusoid curve without using a calculator.
b. What is the earliest time of day at which the water level is just at the top of the post?
c. At the time you calculated in part b, is the post just going under water or just emerging from the water? Explain.
d. When d is negative, the tide is completely out and there is no water at the post. Between what times is the entire post out of the water?
1 answer
1 answer