Question

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of π/12. Trace the circle to find the sine and cosine of the angle to the nearest ten-thousandth.

5π/3

sin 5π/3 =
cos 5π/3 =

How do I do this on a TI-83 Plus calc? Thanks.

Answer 1

first you need to convert to parametric mode

Answer 2

hit the "mode" button, then scroll down to the row that says "Func Par Pol Seq"

Answer 3

after that, highlight "Par" to convert to parametric mode

Answer 4

tell me when you've done that

Answer 5

Ok I did it to that step

Answer 6

now you hit the "y=" button at the top left of the calculator

Answer 7

You'll see things like

X1T =
Y1T =

X2T =
Y2T =

X3T =
Y3T =

etc etc

Answer 8

ok I see it.

Answer 9

in the X1T line, type cos(T)

the T can be found by pressing the button next to the "alpha"

Answer 10

on the Y1T line, you type in sin(T)

Answer 11

ok I did it

Answer 12

now hit "graph" on the top right

Answer 13

a circle should show up

Answer 14

No circle showed up.

Answer 15

ok hit "zoom", then hit 7 (for zoom trig)

Answer 16

Nothing happened

Answer 17

you typed cos(T) and sin(T) in right?

Answer 18

Yes

Answer 19

btw you don't use the T button found above number 4

you use the T found under the "link" text in yellow

Answer 20

Yea that's what I used.But nothing happens

Answer 21

ok what do you see when you bring up the table

Answer 22

In T column it starts with 89.4. In X1T column it shows .01047 and in the Y1T column it starts with .999995. Theres a list of more numbers underneath those columns

Answer 23

ok the table is correct, not sure why the graph isn't showing up

Answer 24

what is your graph window?

Answer 25

Im sorry, I don't understand what you means by what is my graph window.

Answer 26

you get the window by hitting the "window" button (to the right of the "y=" button)

Answer 27

you should see

Tmin
Tmax
Tstep

etc

Answer 28

Sorry mistake one sec

Answer 29

that's ok, take your time

Answer 30

Tmin=0
tmax=6.2831853...
tstep=0.1308996...
xmin=-352.5
xmax=352.5
xscl=90
ymin=-4
ymax=4
yscl=1

Answer 31

ah i see now

Answer 32

thanks

Answer 33

No prob

Answer 34

your xmin and xmax are way too big

Answer 35

make xmin = -6.15 and xmax = 6.15

that's what I have

Answer 36

make xscl = 1.57079

Answer 37

Ok I did it.

Answer 38

now graph

Answer 39

you should see a circle now

Answer 40

Nothing happens

Answer 41

ok try this

Answer 42

hit zoom, then hit 6

after it finishes loading

hit zoom, then hit 7

Answer 43

Ok I get a small ellipsed shaped circle when I hit 6, but I get nothing when I hit 7

Answer 44

weird, I see a circle for 7

Answer 45

ok go back to 6 if that works for you

Answer 46

Ok I hit 6. Is it ok if I hit 2 till i get close up?

Answer 47

yeah do whatever works best for you

Answer 48

Ok I did it.Thanks for the calc guidance. I appreciate it. Can you guide me on this problem. The section this question is based on doesnt mention about parametric equations.

Answer 49

ok now you have the graph set up, hit the "trace" button (to the left of the "graph" button)

Answer 50

since 5pi/3 = 5.2359878 roughly, this means you're going to hold the right arrow key on the calculator until T is equal (roughly) to 5.235987

Answer 51

My calc is giving it in degrees. How do I change it to radians?

Answer 52

hit "mode", then on row three you'll see "Radian Degree"

Answer 53

oh and instead of holding down the button til you reach 5.235987, you can type in 5pi/3 into the trace feature (which is much faster)

Answer 54

ok got it to 5.23....

Answer 55

what are the x and y values

Answer 56

x=.5 and y=-.8660254

Answer 57

perfect on both

Answer 58

x was cosine, so cos(5pi/3) = 0.5

y was sine, so sin(5pi/3) = -0.8660254

Answer 59

That's it! Awesome Thanks for your help! I appreciate it!

Answer 60

glad to be of help, yw

Answer 61

^^

Answer 62

oh and i figured out why your window was giving -352 and 352 for xmin and xmax

if you are in degree mode, it does this (probably because that's near 360?)

but if you switch to radian mode, then follow these steps

step 1) hit zoom
step 2) hit 6
step 3) wait til it fully loads
step 4) hit zoom
step 5) hit 7

it should work...at least I got it to work

Answer 63

Ok thank you for the information. Big help! ^^

Answer 64

sure thing