Explanation
To find the values of t for which y=0, we need to solve the equation:
y=3.50sin(t)+1.20sin(2t)=0
When sin(t)=0, it means t=nπ, where n is an integer.
Next, consider the term sin(2t)=0, which leads to 2t=nπ, or t=2nπ.
Case 1: t=nπ
Substituting t=nπ into the equation:
y=3.50sin(nπ)+1.20sin(2nπ)=3.50(0)+1.20(0)=0
Case 2: t=2nπ
Substituting t=2nπ into the equation:
y=3.50sin(2nπ)+1.20sin(nπ)=3.50sin(2nπ)+1.20(0)
To find the values of n for which y=0, we set sin(2nπ)=0.
This occurs when n is an even integer.
Conclusion:
The first two values of t for which y=0 are:
t=0 seconds and t=π seconds
