Question

at which x - value does the cosine function attain a maximum value?
$x = 0$
$x=\frac{pi}{2}$
$x = 1$
$x=\frac{3pi}{2}$

Explanation:

Step1: Recall the range of the cosine function

The range of \(y=\cos(x)\) is \([- 1,1]\).

Step2: Calculate the value of \(\cos(x)\) for each option

• For \(x = 0\), \(\cos(0)=1\).
• For \(x=\frac{\pi}{2}\), \(\cos(\frac{\pi}{2}) = 0\).
• For \(x = 1\) (in radians), \(\cos(1)\approx0.54\).
• For \(x=\frac{3\pi}{2}\), \(\cos(\frac{3\pi}{2})=0\).

Since the maximum value of the cosine function is \(1\) and it occurs when \(x = 0\) (and \(x = 2k\pi,k\in\mathbb{Z}\)), the answer is \(x = 0\).

Answer:

A. \(x = 0\)