tan x intercepts

jagguy
jagguy used Ask the Experts™
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Hi,
Finding the x intercepts for a tan graph like 3tan(2x)  ?
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tan(x)  is 0, where n is any integer, at

0, 180, 360...., n*180,......

3tan(2x) = 0

Gives

        2x = n*180

          x =n*90      for any integer n

or

5tan(4x+60) =0


        4x+60 = n*180

                 x = n*45 - 15      for any integer n


Hint: When trying to do these trigonometric equations it is really good idea to use their graphs to get a feel of what they are doing., eg HERE. Commit their shape to memory, I refer to them constantly when doing trig work.

(It is better that you do your work in radians rather than degrees btw)
you want the x crossings of
3tan(2x) =0   ??

note that tan(2x) = 0 also.
to simplify things let z = 2x

Then you have
tan(z)
and you can immediately use the nice graphs in the link that gwenforweb gave you

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