Sine And Cosine Integrals - Texas Instruments TI-89 Tip List

To put either of the roots in the history display, use a list index of [1] or [2] as needed:
{0.5,0.25}[1]
{0.5,0.25}[2]
The TI92 operation mode should be set to APPROXIMATE, since the purpose of quadrtic() is to reduce
floating-point arithmetic errors. If you need exact answers, the classical solution equations are just as
good. If quadrtic() is run with the mode set to EXACT, it may take a very, very long time to return the
answers.
For example, let a = 1E-400, b = -6 and c = 1. The classic solution gives
x1 = 6E400
x2 = 0
The improved solution equations give
x1 = 6E400
x2 = 0.1666...
The improved method gives a better root for x2.
Note that the built-in zeros() function on the TI92+ gives the same results as the classical method.
quadrtic() will return complex results if the complex format is set to RECTANGULAR or POLAR.
Otherwise, equations with complex results will result in an execution error.
quadrtic() returns these solutions for combinations of a=0, b=0 and c=0:
a=0
b=0
c=0
a=0 and b=0
b=0 and c=0
a=0 and b=0 and c=0

[6.33] Sine and cosine integrals

The sine and cosine integrals are functions which sometimes come up in integration and engineering
applications. For example, the sine integral shows up when evaluating the radiated power of antennas,
and some hypergeometric functions The sine integral is called Si(z), and the cosine integral is called
Ci(z). They are usually defined as
Si ( z ) =
or sometimes defined as
Si ( z ) = ✜ 2 −
puts 0.5 in the history display
puts 0.25 in the history display
y1 = 1
y2 = 1
y1 = 1
y2 = 0
root 1 undefined, root 2 is solution to bx+c=0
two identical real roots, or 2 conjugate roots
one root is zero
both roots are undefined; returns {undef undef}
returns 0 and 'undef'
both roots are undefined
z sin ( t )
¶
dt
0 t
∞ sin ( t )
¶
dt
z t
z cos ( t ) −1
¶
Ci ( z ) = ✏ + ln ( z ) +
0 t
∞ cos ( t )
¶
Ci ( z ) = −
dt
z t
dt
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