Trig help needed here!

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mathfun

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Dec 26, 2005
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Q1- Evaluate: cot(-2.3)
what i've got so far is: tanx= -1/2.3, which is -.4101. However, on the solutions page, it says that cotangent is negative in quad II & IV, which i understand, but then it says "therefore, the 2nd quadrant answer is pi-0.4101 and the fourth quadrant answer is 2pi - 0.4101. "how come?? Why would you want the answers to be in the negative quadrants? and how do you know to use pi and 2pi to minus?

Q2- When the graph of y=sinx and y=cosx are drawn, 0<=x<2pi, in which quadrants do they intersect? The answers are Quad I and III. But when i graphed them on my calculator.. they intersect in all four quadrants! how come?? please explain!

Please help me so I can continue my math homework. Thanks so much.
 
Q1 - I presume you mean cot(x) = -2.3 In order for the inverse relations to be FUNCTIONS, they must be restricted. The Range of the function f(x) = atan(x) is (-pi/2,pi/2). The Range of the function f(x) = acot(x) is (0,pi). You must reconcile this difference as you go through the problem.

You are given cot(x) = -2.3 The cotangent is negative only in quadrants II and IV. No matter how you find your REFERENCE angle, you must not give an answer that is not in either Quadrant II or Quadrant IV.

Q2 - You simply drew them incorrectly. There are no intersections in Quadrants II and IV. They have opposite signs! Check your graphing technique. You should find some setup problem. How many periods do you get? Are you in Radians?
 
no, i don't mean cotx=2.3
i mean cot(2.3)

Q2. i graphed them on my calculator... and then zoom, trig.
 
This says to me:

Q1: Then you are not making any sense at all. Why do you think tan(x) = -1/2.3 is a step in the right direction?

Q2: You do not know what your calculator is doing.

I think you'll have to do better than that. :(
 
Now you have really got me confused.

the question is RIGHT from the book is "Evaluate cot(-2.3)" On the solutions page this is what they have:
cotx=-2.3 -> 1/tanx = -2.3n -> tanx = -1/2.3
ETC.

I don't understand how they went from cot(2.3) to cotx=2.3 either.
Are you saying the book isn't making any sense???

Q2: Of course I don't know what my calculator is doing. Why else would I be on this board asking for help?!?!
what i plugged in my calculator was y=sinx and y=cosx and then look at the intersections.

I think you'll have to do better than that in order to help people who need help. Thanks a lot for putting my self-esteem down.
 
You want 0 <ans<2pi
I think the best way to see this is by graphing using
WINDOW
x<sub>min</sub> = 0
x<sub>max</sub> = 2pi
x<sub>scl</sub> = pi/2
y<sub>min</sub> = -4
y<sub>max</sub> = 4
y<sub>scl</sub> = 1
Y=
Y<sub>1</sub> = 1/tan(x)
Y<sub>2</sub> = -2.3

Where they intersect are the two answers.
Don't zoom it. You want to see only (0,2pi)
 
1) If you're finding the value(s) "x" for which cot(-2.3) = x, then why would you switch to "tan(x) = -1/2.3"? Shouldn't you be working with "1/tan(-2.3) = x"?

You ask "how come?" "How come" what? How come the values of tangent are negative in the second and fourth quadrants? Or something else? Please be specific.

You also ask about using "pi" in the answer. Your statement that the answer requires "pi" is likely what led the other tutor to assume that you'd posted the answer incorrectly. There would be no need for "pi" in the answer to "find the value of cot(-2.3)"; there would be a need for "pi" in the answer to "solve cot(x) = -2.3".

2) Since we can't see what you've entered into your calculator, we would have no way of knowing what sort of graph you may be looking or, nor why.

Please reply with the specifics of what you've done. The exact functions you've entered into your calculator would be helpful. (Since "ZOOM" "Trig" only changes the axis markings from integers to portions of "pi", clicking these options would not have anything to do with what your graphs look like.)

Thank you.

Eliz.
 
2) Y=
i put in:
Y1=sin(x)
Y2=cos(x)

ZOOM, TRIG, and then looked at the intersections

Please tell me what I'm doing wrong.

Also, does it matter which mode I am in when i graph it? cuz I've noticed that in both radian and degree mode, the graph is the same.
 
1) I don't know. According to my textbook, it says "evaluate cot(-2.3)"
solutions: "cotx = -2.3 -> 1/tanx = -2.3 -> tanx = -1/2.3

Once at this step, set calculator to radian mode and tan-1(-1 / 2.3) and press enter. Calculator should read -0.4101. Cotangent is negative in quadrant II and IV, and the answer should be between 0<_x<2pi. Therefore, the second quadrant answer is pi-0.4101 and the fourth quadrant answer is 2pi-0.4101. So the answers are 2.73 and 5.87.

Thats the whole solution. I'm really confused. If you're wondering, the textbook is "Student work book. Theory and Problems for senior high math. Revised third edition. Auth or: R.J. Mickelson."
 
As I said, don't zoom it. You see (-2pi,2pi) when you do that. The left half is not of interest to you. You want (0,2pi) as I set up in WINDOW
-------------
Gene

PS That's why I suggested graphing. Putting 1/tan(-2.3) gives only one answer. The graph shows both.
----
G
 
Thanks Gene.

However, the answer is quadrant I and III. But on my calculator, since there is no left side, it only shows quadrant I and IV.
 
Did you set up WINDOW as I said? Mode = radians? My TI shows quads I, II, III & IV split by scl = pi/2.
I get your two answers at the intersections.
2.7314653 in quad II & 5.873058 in quad IV
 
yes, i've done exactly what you've plugged in, but i'm still only getting quadrants I and IV.

however, I was talking about #2.

Sigh..this is so hopeless.
 
mathfun said:
1) According to my textbook, it says "evaluate cot(-2.3)" solutions: "cotx = -2.3....
Click to expand...
These two statements, "evaluate cot(-2.3)" and "solve cot(x) = -2.3", are not the same thing. If this is really what the book says, then you need to ask your instructor which meaning you're supposed to use, the actual question ("evaluate") or the expected response ("solve"), as the answers to the two are not the same.

mathfun said:
Y=, i put in Y1=sin(x), Y2=cos(x). ZOOM, TRIG, and then looked at the intersections Please tell me what I'm doing wrong.
Click to expand...
The original exercise asks only for the intersections on the interval from zero to 2pi. Why are you looking at other intervals? Just follow the given instructions.

mathfun said:
Also, does it matter which mode I am in when i graph it?
Click to expand...
Probably not. But since the exercise is given in terms of radians, using this form for your answers is probably expected.

Eliz.
 
I'm so confused. Same setup for #2 except y=-1 to 1 and the sine & cos in Y=. NO ZOOM. You can't be getting quads I & IV with those numbers, you just can't. You do have a TI, don't you?
 
stapel said:
These two statements, "evaluate cot(-2.3)" and "solve cot(x) = -2.3", are not the same thing. If this is really what the book says, then you need to ask your instructor which meaning you're supposed to use, the actual question ("evaluate") or the expected response ("solve"), as the answers to the two are not the same.
Click to expand...
solve means solving for x. what does evaluate mean?

stapel said:
The original exercise asks only for the intersections on the interval from zero to 2pi. Why are you looking at other intervals? Just follow the given instructions.
Click to expand...
if i change my window to what gene said, it only shows quadrant I and IV. If i'm talking about #2, answers being quadrant I and III. how can i even see quadrant III?
 
Gene said:
I'm so confused. Same setup for #2 except y=-1 to 1 and the sine & cos in Y=. NO ZOOM. You can't be getting quads I & IV with those numbers, you just can't. You do have a TI, don't you?
Click to expand...

Yes, i do have a TI.
for #2 WINDOW here is what i have.
Xmin=0
Xmax=2pi
Xscl=pi/2
Ymin=-1
Ymax=1

Y=
Y1=cos(x)
Y2=sin(x)

when i press graph, it only shows quadrant I and IV.
 
First push graph then push trace. You should see x=? at the bottom of the screen. What does it say?
 
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