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Can someone do a calculation on a TI Inspire CAS?
01-30-2019, 09:18 AM (This post was last modified: 01-30-2019 09:20 AM by EdS2.)
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RE: Can someone do a calculation on a TI Inspire CAS?
For those still unsure, the key here is that 3.1415926534 is not pi, it is an approximation to pi. So, an exact calculation of sin(x) using this number should not be zero - it should be approximately zero. (Edit: whereas sin(180) in degree mode should be exactly zero.)

Interestingly enough, HP themselves said the same thing, in 1976:

Quote:There is a point where the new algorithms appear at first glance to be less accurate. If we calculate tan π in radians, the answer is 4.10 E -10 on the HP-91 whereas the HP-55 yields 0. This is misleading, for π on the keyboard should really be labeled π₁₀, showing that it is ten digits of π. Thus
  • π₁₀ = 3.141592654
To ten digits, tan π₁₀ = 4.120676150 E -10. One can see that the HP-91 gives the better answer to this problem.

The reason that the HP-91 does not give the correct answer is that prescaling is done with a finite-length π. To give the correct answer to this problem, a π of length 20 would have to be used. It can be shown that to produce the correct answer to all trigonometric problems in radian measure, it takes a π of length 120. The HP-91 actually uses 13 digits of π.
The New Accuracy: Making 2³ = 8, by Dennis. W. Harms
in HP Journal, November 1976 page 17.
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RE: Can someone do a calculation on a TI Inspire CAS? - EdS2 - 01-30-2019 09:18 AM

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