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Answer on Trigonometry Question for Wayne

Question #8078
how do I graph y=2tan2x
Expert's answer
First of all you graph tan(x) (red graph on the picture)
Then you squeeze it twice and obtain tan(2x) (green curve on the picture)
Then you strech it vertically twice and obtain 2tan(2x) (blue curve on the picture - final result)
<img src="data:image/png;base64,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" 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