at which x - value does the cosine function attain a maximum value?\n$x = 0$\n$x=\frac{pi}{2}$\n$x =…
at which x - value does the cosine function attain a maximum value?\n$x = 0$\n$x=\frac{pi}{2}$\n$x = 1$\n$x=\frac{3pi}{2}$
Answer
Answer:
A. (x = 0)
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).