Determine if the statement is true or false. All solutions of \( \tan x=-1 \) are given by \( x=-\frac{\pi}{4}+n \pi \) for any integer \( n \). Choose the correct answer below. A. False, because \( x=\tan ^{-1}(-1) \) is in the interval \( (0, \pi) \), that is, \( \tan ^{-1}(-1)=\frac{\pi}{2} \). So, all solutions of \( \tan x=-1 \) will be \( x=\frac{\pi}{2}+n \pi \). False, because \( x=\tan ^{-1}(-1) \) is in the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), that is, \( \tan ^{-1}(-1)=-\frac{\pi}{2} \).So, all solutions of \( \tan x=-1 \) will be \( x=-\frac{\pi}{2}+2 n \pi \). True, because \( x=\tan ^{-1}(-1) \) is in the interval \( (0, \pi) \), that is, \( \tan ^{-1}(-1)=\frac{\pi}{4} \cdot \) So, all solutions of \( \tan x=-1 \) will be \( x=-\frac{\pi}{4}+n \pi \) C. D. True, because \( x=\tan ^{-1}(-1) \) is in the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), that \( \mathrm{si}, \tan ^{-1}(-1)=-\frac{\pi}{4} \). So, all solutions of \( \tan x=-1 \) will be \( x=-\frac{\pi}{4}+n \pi \)
UpStudy ThothAI Solution
Quick Answer
Step-by-step Solution
Enter your question here…