Question

If the angle made by the tangent at the point \((x_0, y_0)\) on the curve \(x = 12(t + \sin t \cos t)\), \(y = 12(1 + \sin t)^2\), with \(0<t<\frac{\pi}{2}\), with the positive x-axis is \(\frac{\pi}{3}\), then \(y_0\) is equal to:

• A. \(6(3 + 2\sqrt{2})\)
• B. \(3(7 + 4\sqrt{3})\)
• C. 27
• D. 48

Hint:

To solve problems involving parametric curves and slopes, always recall the derivative formulas and use the trigonometric identities to simplify expressions.