Getting started TI-85/86 calculators, 4
Example 7 Attempt to evaluate
√
4π by entering
√
4π
Solution The TI-85 calculator reads
√
4π 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 = 2π
.
= 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 t h e 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 decim al 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 whe n 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 5x
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 t able in addition to −15
do you re cognize as exact?
x y = 5x
1/3
.
= x y = 5x
1/3
.
=
−27 −15 −30 −15.5361625298
4 10
6 8
Solution You can do these calculations more e ffic iently by storing the formula for the function.
Press GRAPH F1 to access the y(x) = menu and CLEAR to erase any previous
formula for y1. Press 5 x−V AR ∧ ( 1 ÷ 3 ) to have y1 = 5x ∧ (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 STOI x−V AR 2nd : 2nd ALPHA Y
ALPHA ALPHA 1 so the screen reads −27 → x: y1. The colon (above the period
key) separates the two commands on the one line. Then press ENTER for the value
−15 of y1 at x = −27.
Press 2nd ENTRY to d isplay the last line again, use J to move the cursor to
the 2 and press 3 0 to have −30 → x: y1. Press ENTER for the approximate decimal
value −15.5361625298 of y1 at x = −30.
Press 2nd ENTRY t o display the last line again, use J to move th e cursor
to the minus sign and press 4 DEL DEL to have 4 → x: y1. Press ENTER for the
approximate decimal value 7.93700525984 of y1 at x = 4.
Press
2nd ENTRY to display t h e last line again, use J to move the cursor to
the 4 and press
1 2nd INS 0 to have 10 → x: y1. Press ENTER for the approximate
decimal value 10.7721734502 of y1 atx = 10.
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