2. (1 point) The first minimum along positive x-axis of y=2cos(3x) occurs at: x=90^circ x=60^circ x=0^circ d. x=180^circ

To determine the first minimum of the function \( y = 2 \cos(3x) \) along the positive \( x \)-axis, we need to analyze the behavior of the cosine function.<br /><br />---<br /><br />### Step 1: General form of cosine minima<br />The cosine function \( \cos(kx) \) has minima when:<br />\[<br />\cos(kx) = -1<br />\]<br />This occurs at:<br />\[<br />kx = (2n+1)\pi, \quad n \in \mathbb{Z}<br />\]<br />where \( n \) is an integer. Solving for \( x \), we get:<br />\[<br />x = \frac{(2n+1)\pi}{k}<br />\]<br /><br />For our specific function \( y = 2 \cos(3x) \), the value of \( k = 3 \). Therefore, the minima occur at:<br />\[<br />x = \frac{(2n+1)\pi}{3}, \quad n \in \mathbb{Z}<br />\]<br /><br />---<br /><br />### Step 2: First minimum along the positive \( x \)-axis<br />The first minimum corresponds to \( n = 0 \):<br />\[<br />x = \frac{\pi}{3}<br />\]<br /><br />---<br /><br />### Step 3: Convert to degrees<br />Since \( \pi \) radians equals \( 180^\circ \), we convert \( x = \frac{\pi}{3} \) to degrees:<br />\[<br />x = \frac{180^\circ}{3} = 60^\circ<br />\]<br /><br />---<br /><br />### Final Answer:<br />The first minimum along the positive \( x \)-axis occurs at:<br />\[<br />\boxed{x = 60^\circ}<br />\]<br /><br />Correct option: **b. \( x = 60^\circ \)**