9. -/1 points details my notes oscat1 8.1.040. let f(x) = cos(x). find the x - intercepts of f(x) on 0, 2π)…

9. -/1 points details my notes oscat1 8.1.040. let f(x) = cos(x). find the x - intercepts of f(x) on 0, 2π). (x, y) = ( ) (smaller x - value) (x, y) = ( ) (larger x - value) additional materials ebook graphing sine and cosine transformations

9. -/1 points details my notes oscat1 8.1.040. let f(x) = cos(x). find the x - intercepts of f(x) on 0, 2π). (x, y) = ( ) (smaller x - value) (x, y) = ( ) (larger x - value) additional materials ebook graphing sine and cosine transformations

Answer

Explanation:

Step1: Set the function equal to 0

Set $y = f(x)=\cos(x)=0$.

Step2: Recall the cosine - zero points

We know that $\cos(x) = 0$ when $x=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$.

Step3: Find values in the given interval

For $k = 0$, $x=\frac{\pi}{2}$; for $k = 1$, $x=\frac{\pi}{2}+\pi=\frac{3\pi}{2}$ in the interval $[0,2\pi)$.

Answer:

$(x,y)=\left(\frac{\pi}{2},0\right)$ (smaller $x$-value) $(x,y)=\left(\frac{3\pi}{2},0\right)$ (larger $x$-value)