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lrdheat · 12-27-2019, 04:29 AM

I have the Nspire CAS IPad app...when graphing 1/((tan 2*x)^(sin 2*x)), I get the expected real part of the graph, but, surprisingly, a messy mash of graphing where there is no real solution. Is this to be expected, or do I have some setting that needs to be changed?

ijabbott · (This post was last modified: 12-27-2019 09:43 PM by ijabbott.)

(12-27-2019 04:29 AM)lrdheat Wrote: I have the Nspire CAS IPad app...when graphing 1/((tan 2*x)^(sin 2*x)), I get the expected real part of the graph, but, surprisingly, a messy mash of graphing where there is no real solution. Is this to be expected, or do I have some setting that needs to be changed?

If you change the Document Settings, Real or Complex setting to something other than "Real" (i.e., change it to either "Rectangular" or "Polar"), then the graph will only show the parts where the principal value is real.

In Real mode, it seems to treat the approximate value of (sin(2*x)) as a rational number and magics up a real result when (tan(2*x)) is negative. For example, when x is 1, so 2*x is 2, tan(2) is approx -2.1850398632615, sin(2) is approx 0.90929742682568, and (-2.1850398632615)^0.90929742682568 produces a real result of approx 2.03549259451, and 1/2.03549259451 is approx 0.491281571202, so the graph plots a point at (1, 0.491281571202) even though the principal value is complex.

In Rectangular mode, 1/((tan(2))^(sin(2))), approx 1/((-2.1850398632615)^0.90929742682568) produces a complex result of approx -0.471470916087-0.138104154488*i, so no point is plotted on the graph for x=1.

lrdheat · 12-28-2019, 05:07 AM

Interestingly, on the Prime (CAS), taking TAN (-.6) and SIN (-.6) both yield non complex results...if I take the result for TAN (-.6) and raise it to the result of SIN (-.6), a non complex result comes up. However, if I type in TAN(-.6)^SIN(-.6), I get a complex result!

The Prime plots the non complex portion of the graph in Function App, and the real and complex portion of the graph in the Advanced Graph App...the Prime does not attempt to connect the dots, and has an uncluttered graph, but was still surprised that the complex portion of the graph appeared.

The CASIO fx-CG 50 plots only the real portion of the graph.

Joe Horn · 12-28-2019, 10:47 AM

(12-28-2019 05:07 AM)lrdheat Wrote: ...if I take the result for TAN (-.6) and raise it to the result of SIN (-.6), a non complex result comes up. However, if I type in TAN(-.6)^SIN(-.6), I get a complex result!

Not really. The algebraic "order of operations" demands that powers are done before leading negative signs (see the bottom two entries in the screen shot below). Try putting the result of TAN(-.6) in parentheses before raising it to the power, and you'll see the complex result you're expecting, like this:

[Image: power.png]

lrdheat · 12-28-2019, 03:44 PM

Thanks, Joe!

lrdheat · 12-28-2019, 05:13 PM

One thing that I like on my G2 Prime graphing vs emulator of TI Nspire CAS is that the Prime makes it easy to enter the endpoints of an integral, and accepts the limiting case in a problem such as the above of 0 and pi/4. On the TI, if I set the endpoints as on the Prime, in the graphing environment, it will not allow for the integration due to the function being undefined at these endpoints. In the calculation mode, of course, the integral works.

lrdheat · 12-30-2019, 10:00 PM

One more TI Nspire question (cannot seem to find documentation on this)...in the graphing environment, is there any way to directly type in the lower and upper limit of an area under a curve (integral) as opposed to trying to estimate it by dragging the boundary on the graph?

ijabbott · (This post was last modified: 12-30-2019 10:35 PM by ijabbott.)

(12-30-2019 10:00 PM)lrdheat Wrote: One more TI Nspire question (cannot seem to find documentation on this)...in the graphing environment, is there any way to directly type in the lower and upper limit of an area under a curve (integral) as opposed to trying to estimate it by dragging the boundary on the graph?

Yes, you just type in the numbers when it asks for "Upper bound?" and "Lower bound?" (at least for OS 4.5 on the original CX).

Oh, and Nspire documentation sucks!

lrdheat · 12-30-2019, 10:49 PM

Hi, Ian,

On my IPad app, I do not see a way to get a keyboard to appear where I can type my limits in. The gear shaped icon on the top bar, when I get the graph of interest to flash, only gives the option of dragging the vertical line to my limits, and it is not exact. There must be a way to do this directly in the graphing environment, and I must be blind to it!

ijabbott · 12-31-2019, 12:10 PM

(12-30-2019 10:49 PM)lrdheat Wrote: Hi, Ian,

On my IPad app, I do not see a way to get a keyboard to appear where I can type my limits in. The gear shaped icon on the top bar, when I get the graph of interest to flash, only gives the option of dragging the vertical line to my limits, and it is not exact. There must be a way to do this directly in the graphing environment, and I must be blind to it!

I've only used the real calculator, where the keyboard is always visible! If there isn't a way to enter the bounds directly, a workaround would be select one of the points on the axis afterwards, use the context menu to add coordinates to the point, then select the text of the x coordinate to edit it. Since the integral is tied to these points, it should be updated automatically when it is edited. There is probably an easier way though.