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? Have I rounded it correctly?
To find the displacement when t = 1.45, you can substitute the value of t into the equation y(t) = 2 cos 6t and evaluate it.
y(1.45) = 2 cos(6 * 1.45)
= 2 cos(8.7)
To find the value of cos(8.7), you can use a scientific calculator or a calculator with a trigonometric function button.
Using a calculator, cos(8.7) is approximately 0.5551.
Now, substitute the value of cos(8.7) back into the equation:
y(1.45) = 2 * 0.5551
Multiply the values:
y(1.45) ≈ 1.1102
Rounding to four decimal places, the displacement when t = 1.45 is approximately 1.1102 centimeters.
So, the answer rounded to four decimal places is 1.1102.