The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t) = 2 cos 6t, where y is the displacement in centimeters and t is the time in seconds. Find the displacement when t = 1.45, and round your answer to four decimal places if necessary.
1.9770?
I get -1.4973
assuming the angle is in radians
If it is in degrees I get
1.9770
Since the displacement is in centimeters it probably is positive.
To find the displacement when t = 1.45, we can substitute the given value of t into the equation y(t) = 2 cos 6t:
y(1.45) = 2 cos (6 * 1.45)
To evaluate cos (6 * 1.45), we need to find the cosine of 6 times 1.45.
First, multiply 6 by 1.45:
6 * 1.45 = 8.7
Now, we find the cosine of 8.7 using a calculator or trigonometric table. The cosine of 8.7 is approximately 0.08716.
Substituting this value into the equation:
y(1.45) = 2 * 0.08716
y(1.45) = 0.17432
Rounding this answer to four decimal places gives:
y(1.45) ≈ 0.1743
Therefore, the displacement when t = 1.45 is approximately 0.1743 centimeters.