select all that are x - intercepts of the tangent graph.\n$\frac{pi}{4}$\n$\frac{pi}{2}$\n$pi$\n$\frac{3pi}{2…
select all that are x - intercepts of the tangent graph.\n$\frac{pi}{4}$\n$\frac{pi}{2}$\n$pi$\n$\frac{3pi}{2}$\n$3pi$\ndone
Answer
Explanation:
Step1: Recall tangent - function property
The tangent function is (y = \tan(x)=\frac{\sin(x)}{\cos(x)}). The (x) - intercepts of (y = \tan(x)) occur when (\sin(x)=0) and (\cos(x)\neq0).
Step2: Analyze each option
- For (x = \frac{\pi}{4}), (\tan(\frac{\pi}{4})=1\neq0).
- For (x=\frac{\pi}{2}), (\cos(\frac{\pi}{2}) = 0), and (\tan(x)) is undefined at (x=\frac{\pi}{2}).
- For (x=\pi), (\sin(\pi)=0) and (\cos(\pi)= - 1\neq0), so (\tan(\pi)=0).
- For (x = \frac{3\pi}{2}), (\cos(\frac{3\pi}{2})=0), and (\tan(x)) is undefined at (x=\frac{3\pi}{2}).
- For (x = 3\pi), (\sin(3\pi)=0) and (\cos(3\pi)=-1\neq0), so (\tan(3\pi)=0).
Answer:
(\pi,3\pi)