Trigonometry on the TI-83
After reading this page, you should do HW 3, Supplement 3.
Like all scientific and graphing calculators, your
TI-83 has
two modes of angle measure: degrees and radians. Whenever you do
a calculation
that uses a trigonometric function (like sin) or an inverse
trigonometric
function (like 
), you need to make
sure
that your calculator is in the correct mode. To change modes in
the TI-83,
follow these steps: (1) From the main screen, press the [MODE] key; (2)
On the
mode screen, you will see that a number of options can be
adjusted. Angle
measure is on the third row. Use the down arrow key to move to
this row; (3)
Use the left and right arrow keys to change between radians and
degrees. When
the mode that you want is selected (the cursor is blinking on the word
radians
or degrees), press [ENTER]; (4) Press [2nd][MODE] (this key
combination, QUIT, is very useful) to get back to the main
screen. Your
calculator is now in the mode that you selected.
Note: When you are converting between degrees and radians (by multiplying by pi/180 or 180/pi), it does not matter what mode your calculator is in, because you are not using a trig function or inverse trig function.
Example. Evaluate 
.
Solution. Make sure that
your calculator is in degree mode; on a blank line on the main screen
use the
key sequence: [SIN][1][5][)][ENTER]. Ans: approx. 0.2588
Example: Evaluate sin(4.25). Solution: Make sure that your calculator is in radian mode (How do we know this is a radian problem? There are no units given on the angle, and that always means that the units are radians). [SIN][4][.][2][5][)][ENTER]. Ans: approx. -0.8950
Solving for an angle
Example. Solve for 
:
Note. It is very useful to understand that
this is, in
essence, exactly the same kind of problem that we’ve done before, on
the page
Trigonometry Review,
but there we could use a special triangle to find the
reference angle. The only real difference now is that we need to
use the calculator
to find the reference angle, because is not found
in a special
triangle.
Solution.
(1) Check that you’re in degree mode
(2) Decide in what two quadrants you have answers:
in this
case, there are answers in quadrants I and IV, say 
and
, resp., since
these are the two quadrants where cos is positive
(3) Use the inverse cos function to find the
reference angle:
;
key sequence: [2nd][COS][.][5][6][7][8][)][ENTER]
(4) Use the formulas from Trigonometry Review to find the answers:
Quadrant I: 
Quadrant II: 
The following is another example. It is essentially the same type of problem. But pay attention to these differences: it is a radian problem, the trig function, cot, is not one of the three we have on the calculator, and the given value is negative.
Example. Solve for 
:
.
Since we’re not going to find in
a special triangle, we
have to use the calculator again to find the reference angle.
Solution.
(1) Check that you’re in radian mode
(2) Change to a tan problem (because we don’t have
inverse
cot on calculator): 
(3) Decide in what two quadrants you will have
answers: in
this case, we have quadrant II and IV answers, say 
and
, resp.,
because these are the two quadrants where cot is negative.
(4) Use your calculator to find the reference
angle. To do
this, use the inverse tangent function (2nd tan) and ignore
the
negative sign, if applicable (we ignore the neg because we need the
reference
angle to be a positive, acute angle): 
; here
is the key sequence
for the reference angle: [2nd][TAN][1][/][2nd][x^2][7][)][)][ENTER]
(5) Use the reference angle, and appropriate formula, depending on quadrant (see Trigonometry Review), to find the two answers (here rounded to 4 decimal places):
Quadrant II: 
Quadrant IV: 
Now you should do HW 3, Supplement
3