Getting started
TI-85/86 calculators, 3
(b)
Press
3
(
4
)
÷
2nd
√
(
3
6
)
−
1
0
÷
(
8
−
3
)
so
the screen reads 3(4)
/
√
(36)
−
10
/
(8
−
3). Then press
ENTER
for the value 0.
The next example shows how using the negation symbol
–
for subtraction can lead to an error
message or give an incorrect result because a product is calculated instead of a difference.
Example 3
Evaluate the expressions 2
π
−
π
, 2
π
–
π
, 8
−
5, and 8
–
5, where
−
is the subtraction
symbol and
–
is the negation symbol. Explain the results.
Solution
The calculator gives 3
.
14159265359
.
=
π
for 2
π
−
π
, which it obtains by subtracting
π
from 2
π
. It gives
−
19
.
7392088022
.
=
−
2
π
2
for 2
π
–
π
, which it interprets as 2
π
multiplied by
−
π
. The expression 8
−
5 equals 3, and you get
−
40 with 8
–
5, which the
calculator either interprets as the product of 8 and
−
5.
The need to use
∗
Because TI-85 and TI-86 calculators allow words to be used for variables, multiplication signs (
∗
) must
be used between letters that represent numbers to be multiplied.
Example 4
Evaluate
AB
with
A
= 5 and
B
= 2 by first storing the values of
A
and
B
.
Solution
Enter
5
STO
I
A
ENTER
2
STO
I
B
ENTER
to store the values. Then enter
ALPHA
A
∗
ALPHA
B
ENTER
for the answer
A
×
B
= 10. (Notice that using
ALPHA
A
ALPHA
B
to write
AB
and then
ENTER
yields an error message since
the variable AB has not been defined.)
The dangers of using improper parentheses
TI-85 and TI-86 calculators interpret certain expressions in unexpected ways because they use the
following modification of Rules 3 through 5.
Rule 6
The taking of powers has priority over the evaluation of functions that appear before their
variables, such as the trigonometric functions, logarithms,
e
x
,
√
, and negation. Also, the parentheses in
expressions such as
sin(2)
and
e
∧
(2)
are ignored.
Example 5
Evaluate sin
3
(2) = (sin(2))
3
.
Solution
The seemingly logical expression sin(2)
∧
3 will not work. By Rule 6, the parentheses are
ignored, leaving sin 2
∧
3. Then the taking of the cube has priority over the evaluation
of the sine function, and the calculator gives 0
.
989358246623
.
= sin(2
3
) = sin(8).
†
For the correct answer, use an extra pair of parentheses by entering (sin(2))
∧
3.
This gives the correct value 0
.
751826944669.
The TI-85 also uses the following two additional modifications of Rules 1 through 5
Rule 7
Multiplication by juxtaposition has priority over division and multiplication represented by
∗
.
Example 6
Attempt to evaluate
1
5
(10) = 2 by entering 1
/
5(10).
Solution
The TI-85 evaluates 1
/
5(10) as 1
/
(50) = 0
.
02 because it uses Rule 7 and multiplies the
10 and the 5 before performing the division. Enter 1
/
5
∗
10 or (1
/
5)(10) instead.
The TI-86 gives
1
5
(10) = 2, as expected, because it does not use Rule 7.
Rule 8
Multiplication represented by juxtaposition, where the second term is a number or a variable,
has priority over the evaluation of functions that appear before their arguments.
†
If you obtained 0
.
13917310096 here, then your calculator is using degrees instead of radians. Press 2nd
MODE , put the
cursor on
<
Radian
>
and press ENTER to select radian mode. Press 2nd
QUIT
2nd
ENTRY to return to the home screen
and recall the last typed line, and then ENTER for the correct answer.
