Questions: Solve for (t, 0 leq t<2 pi). 28 sin(t) cos(t) = -4 sin(t) t =

Solution Steps

Starting with the equation \(28 \sin(t) \cos(t) = -4 \sin(t)\), we can factor out \(\sin(t)\) from both sides, leading to: \[ \sin(t)(28 \cos(t) + 4) = 0 \]

Setting the first factor to zero, we have: \[ \sin(t) = 0 \] The solutions for this equation in the interval \(0 \leq t < 2\pi\) are: \[ t = 0, \quad t = 2\pi \]

Next, we set the second factor to zero: \[ 28 \cos(t) + 4 = 0 \] Solving for \(\cos(t)\), we get: \[ \cos(t) = -\frac{4}{28} = -\frac{1}{7} \] However, this equation does not yield any additional solutions within the specified interval \(0 \leq t < 2\pi\).

The only solutions found are from the first factor: \[ t = 0, \quad t = 2\pi \] Rounding these values to at least two decimal places, we have: \[ t = 0.00, \quad t = 6.28 \]

Final Answer