Graphing a Tan Function


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\(\displaystyle 0 = \tan x\)

\(\displaystyle 0 = \tan (1) x\) - Note \(\displaystyle 1 * x = x\)

\(\displaystyle 0 = \tan x\)

tan(x) is a number.

If you write tan(1), that means x=1, and you're taking the tangent of 1 radian, which is about 1.5574 (rounded to four places).

If you write tan(1)x, that means the number 1.5574 times the number x.

Why are you writing tan(1)x ?

Did you tell us that 1*x = x because you're suggesting that tan(1)x somehow means tan[(1)(x)]?

I'm trying to understand why you told us that 1 times x is x...that kinda goes without saying, does it not?
 

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Find Two More Points to Make an Accurate Graph

The positive and negative versions of \(\displaystyle A\) correspond to the y coordinates of the new points.

\(\displaystyle A = 1\) So our two \(\displaystyle y\) coordinates are \(\displaystyle -1\) and \(\displaystyle 1\)

I don't follow your reasoning on the relationship between A=1 and the y-coordinate of "two more points" on the graph of tan(x). Can you elaborate on what you're thinking?
 

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Connect the [three] Points

Now you have your graph

For somebody who is unfamiliar with the tangent function's behavior, I don't think that 3 points are sufficient to obtain a good graph.

My instructions for plotting tan(x) from scratch would be to build a table of x,y values -- using a calculator to evaluate tan(x) for several values of x within the interval.

Will you please clarify the purpose of your project?
 
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The two asymptotes are \(\displaystyle -\dfrac{\pi}{2}\) and \(\displaystyle \dfrac{\pi}{2}\)

Find the x intercept

\(\displaystyle 0 = \tan x\) ........................................ (1)

\(\displaystyle 0 = \tan (1) x\) - Note \(\displaystyle 1 * x = x\) ... By convention, tan(1)x = [ tan(1) ] * x ..... perhaps you meant to write tan[(1)x]

\(\displaystyle 0 = \tan x\) .... you are repeating line (1)..... what was the purpose of line above! you could have (and should have) started from here.

\(\displaystyle \arctan(0) = 0\)

The \(\displaystyle x\) intercept \(\displaystyle = 0\)


Find Two More Points to Make an Accurate Graph

Three points are not sufficient for any curve - other than a straight line. While drawing a polynomial - you should plot at least two more point than the degree of the polynomial (3 pts for linear, 4 points for parabolic, 5 points for cubic, etc. You have transcendental function - infinite series - you need (in my opinion) at least five points . [/QUOTE].
 
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As pointed out in another thread, didn't take both sides when doing the \(\displaystyle \arctan\) thing. So will update all posts soon.
 
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