Rootfinding (Numerical analysis)?

Question

To help determine the roots of x = tan(x), y = x, and y = tan(x), and look at the intersection points of the two curves

Find the smallest nonzero positive root of x = tan(x) with an accuracy of (error tollerance ε) ε=0.0001

HINT: the desired root is > than pi/2

10 pts. to best! thanks!!

Answer 1

set up a spreadsheet with pi/2 as a constant

column 1 is cell above +  .01 (1, 1.01, 1.02, 1.03, 1.04, etc)

column 2 is (pi/2) * column 1 (x)

column 3 is tan(x)

look for column 2 = column 3 +/- .0001

If that does not get close enough, change column 1 to .001

And so on until you get a match.

Ain't computers wonderful to do all the grunt work?

Answer 2

or you could use Newton's algorithm on [1.6, 4.8] with 1st try near the right hand, say 4.6. On my TI 85 I typed 4.6,then :enter,store x, then : ans-(ans- tan ans) / ( 1 - (cos ans)^-2), enter,enter,enter,enter,enter...10 digits accuracy...{4.4934094579}

Answer 3

On my Ti-84, much like an 83,

go to the menu to graph, and define Y1 = tanx and Y2 = x. Using the "trace" button on the calculator, go to their point of intersection. Like "ted" above me says--

x = 4.4934094579