Getting started
TI-85/86 calculators, 4
Example 7
Attempt to evaluate
√
4
π
by entering
√
4
π
Solution
The TI-85 calculator reads
√
4
π
as
p
(4
∗
π
)
.
= 3
.
54490770181 because it uses Rule 8
and multiplies the 4 and the
π
before taking the square root. Enter (
√
4)
π
or
√
4
∗
π
instead to obtain the correct value 6
.
28318530718.
The TI-86 yields (
√
4)
π
= 2
π
.
= 6
.
28318530718, as expected, because it does not use
Rule 8.
Example 8
Atempt to evaluate sin(5)(10) by entering this expression in the calculator.
Solution
The TI-85 gives the wrong value sin(50)
.
=
−
0
.
262374853704 because it uses Rule 8
and does the multiplication before evaluating the sine. Use sin 5
∗
(10) or (sin 5)(10)
instead.
The TI-86 yields the correct answer 10 sin(5)
.
=
−
9
.
58924274663 because it does not
use Rule 8.
Exact and approximate decimal values of functions
Since some but not all numbers can be represented exactly as finite decimals, it is important to distinguish
exact expressions, such as
1
3
and
π
, from decimal approximations, such as 0
.
33333 and 3
.
14159. You also
need to recognize when coordinates obtained from graphs generated by calculators and computers are
approximations.
Example 4
Use your calculator to complete the table below of ten-digit values of 5
x
1
/
3
=
5
3
√
x
at
x
=
−
27
,
−
30
,
4
,
6
,
8
,
and 10. The value 5(
−
27)
1
/
3
= 5(
−
3) =
−
15 is
exact, but
−
15
.
53616253 is only a decimal approximation of 5(
−
30)
1
/
3
, which cannot
be represented by a finite decimal. Its value to 20 decimal places, for example, is
−
15
.
53616252976929433439
.
Which
y
-values in the completed table in addition to
−
15
do you recognize as exact?
x
y
= 5
x
1
/
3
.
=
x
y
= 5
x
1
/
3
.
=
−
27
−
15
−
30
−
15
.
5361625298
4
10
6
8
Solution
You can do these calculations more efficiently by storing the formula for the function.
Press
GRAPH
F1
to access the
y
(
x
) = menu and
CLEAR
to erase any previous
formula for
y
1. Press
5
x
−
V AR
∧
(
1
÷
3
)
to have
y
1 = 5
x
∧
(1
/
3).
To find the value of the function at
x
=
−
27, press
2nd
QUIT
to return to
the home screen and press
(–)
2
7
STO
I
x
−
V AR
2nd
:
2nd
ALPHA
Y
ALPHA
ALPHA
1
so the screen reads
−
27
→
x
:
y
1. The colon (above the period
key) separates the two commands on the one line. Then press
ENTER
for the value
−
15 of
y
1 at
x
=
−
27.
Press
2nd
ENTRY
to display the last line again, use
J
to move the cursor to
the 2 and press
3
0
to have
−
30
→
x
:
y
1. Press
ENTER
for the approximate decimal
value
−
15
.
5361625298 of
y
1 at
x
=
−
30.
Press
2nd
ENTRY
to display the last line again, use
J
to move the cursor
to the minus sign and press
4
DEL
DEL
to have 4
→
x
:
y
1. Press
ENTER
for the
approximate decimal value 7
.
93700525984 of
y
1 at
x
= 4.
Press
2nd
ENTRY
to display the last line again, use
J
to move the cursor to
the 4 and press
1
2nd
INS
0
to have 10
→
x
:
y
1. Press
ENTER
for the approximate
decimal value 10
.
7721734502 of
y
1 at
x
= 10.
