Step-by-step Solution:

Step 1: Rewrite the Equation Using the double-angle identity \( \sin 2t = 2 \sin t \cos t \), the equation becomes: \[ 3.50 \sin t + 1.20 \cdot 2 \sin t \cos t = 0 \] \[ 3.50 \sin t + 2.40 \sin t \cos t = 0 \] Step 2: Factor Out \( \sin t \) Factor out \( \sin t \): \[ \sin t (3.50 + 2.40 \cos t) = 0 \] This gives two cases: 1. \( \sin t = 0 \), 2. \( 3.50 + 2.40 \cos t = 0 \). Step 3: Solve \( \sin t = 0 \) The solutions to \( \sin t = 0 \) are: \[ t = 0, \, \pi, \, 2\pi, \, \dots \] Step 4: Solve \( 3.50 + 2.40 \cos t = 0 \) Rearrange the equation: \[ 2.40 \cos t = -3.50 \] \[ \cos t = -\frac{3.50}{2.40} = -\frac{35}{24} \] However, \( \cos t \) must satisfy \( -1 \leq \cos t \leq 1 \). Since \( -\frac{35}{24} < -1 \), there are no real solutions for this case. Step 5: Identify the First Two Solutions From \( \sin t = 0 \), the first two solutions are: \[ t = 0, \, \pi \] Step 6: Conclusion The first two values of \( t \) for which \( y = 0 \) are: \[ \boxed{t = 0, \, \pi} \] Correct Answer: \(\boxed{C}\)