\(\displaystyle y = 3\tan2x\)
\(\displaystyle A\) (amplitude) \(\displaystyle = |3| = 3\)
Find \(\displaystyle x\) values:
\(\displaystyle y = 3\tan2x\)
\(\displaystyle -3 = 3\tan2x\) and \(\displaystyle 3 = 3\tan 2x\)
Now, looking at the one on the left:
\(\displaystyle -3 = 3\tan2x\)
\(\displaystyle -1 = \tan2x\) How did this line become the next line? :idea: Now i did notice that the \(\displaystyle \arctan\) of \(\displaystyle -1\) was \(\displaystyle -\dfrac{\pi}{4}\)
\(\displaystyle 2x = -\dfrac{\pi}{4}\)
\(\displaystyle -\dfrac{\pi}{8}\)
Moving on to the other one:
\(\displaystyle 3 = 3\tan2x\)
\(\displaystyle 1 = \tan2x\) How did this line become the next line? :idea: I did notice that the \(\displaystyle \arctan\) of \(\displaystyle 1\) was \(\displaystyle \dfrac{\pi}{4}\)
\(\displaystyle 2x = \dfrac{\pi}{4}\)
\(\displaystyle \dfrac{\pi}{8}\)
Now Plug in \(\displaystyle x\) into the original function to get \(\displaystyle y\) values (you would be plotting 2 points).
Pretty much everything else I understand. At least enough to solve the problem, but maybe not on a deeper level yet.
\(\displaystyle A\) (amplitude) \(\displaystyle = |3| = 3\)
Find \(\displaystyle x\) values:
\(\displaystyle y = 3\tan2x\)
\(\displaystyle -3 = 3\tan2x\) and \(\displaystyle 3 = 3\tan 2x\)
Now, looking at the one on the left:
\(\displaystyle -3 = 3\tan2x\)
\(\displaystyle -1 = \tan2x\) How did this line become the next line? :idea: Now i did notice that the \(\displaystyle \arctan\) of \(\displaystyle -1\) was \(\displaystyle -\dfrac{\pi}{4}\)
\(\displaystyle 2x = -\dfrac{\pi}{4}\)
\(\displaystyle -\dfrac{\pi}{8}\)
Moving on to the other one:
\(\displaystyle 3 = 3\tan2x\)
\(\displaystyle 1 = \tan2x\) How did this line become the next line? :idea: I did notice that the \(\displaystyle \arctan\) of \(\displaystyle 1\) was \(\displaystyle \dfrac{\pi}{4}\)
\(\displaystyle 2x = \dfrac{\pi}{4}\)
\(\displaystyle \dfrac{\pi}{8}\)
Now Plug in \(\displaystyle x\) into the original function to get \(\displaystyle y\) values (you would be plotting 2 points).
Pretty much everything else I understand. At least enough to solve the problem, but maybe not on a deeper level yet.
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