Cumene \( (C_6H_5CH(CH_3)_2) \) is converted to phenol by the cumene hydroperoxide process:
1. Oxidation of Cumene: \[ C_6H_5CH(CH_3)_2 + O_2 \rightarrow C_6H_5C(CH_3)_2OOH \]
2. Acidic Hydrolysis: \[ C_6H_5C(CH_3)_2OOH \xrightarrow{H^+} C_6H_5OH + CH_3COCH_3 \] Thus, cumene is oxidized to cumene hydroperoxide, which undergoes acid hydrolysis to give phenol and acetone as a byproduct.
Explain the construction of a spherical wavefront by using Huygens' principle.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.