Question

Which function has the graph attached inside?

A. y= -tan x
B. y= csc x
C. y= cos x
D. y= cot x

**my answer: D.

but I'm not too sure... :/ is it right?

Answer 1

graph!!

Answer 2

Okay, check its zeros... in particular, it has a zero BETWEEN 0 and pi, right?

Answer 3

y = -tan(x)

y = -tan(0) ... plug in x = 0

y = ??

Answer 4

y= 0 ?

Answer 5

so that means that x = 0 is in the domain of y = -tan(x)

Answer 6

but is x = 0 in the domain of the graph given?

Answer 7

mhmm^
So, if y=-tan x
then at x=0, y should also be zero...
Now, does your graph intersect (0,0) ?

Answer 8

no, it doesn't... so that means it cannot be y= -tan x right?

Answer 9

that's right :)
check the second.

Answer 10

y=csc x

Answer 11

While certainly, we can't check csc 0, we can check others...
for instance,
\[\large \csc \frac\pi 2\]

Answer 12

like plug in 0 where? :/

Answer 13

\[\LARGE \frac1{\sin\frac\pi 2}=\sqrt2\]

Answer 14

into the x part?

Answer 15

You can't plug in zero, because
\[\huge \csc0 = \frac1{\sin 0}=\frac10\]

Answer 16

ohhh i see.. so what do i do to see if csc is or isn't the answer? like if it works or doesn't?

Answer 17

D. y= cot x seems correct.

Answer 18

Look at pi/2, the point in between 0 and pi
Clearly, the function equals zero, at x = pi/2, right?

Answer 19

this graph has x intercepts, so if it was y = csc(x), then

csc(x) = 0

should have solutions

Answer 20

but

csc(x) = 0

1/sin(x) = 0

1 = 0

which is false

so there are no solutions, so y = csc(x) has no x-intercepts

Answer 21

okay, so basically it means that it would be impossible for that to be a solution?

Answer 22

There are only two of the six trigonometric functions which are equal to zero, when x = 0
They are...?

Answer 23

Sorry, when x = pi/2

Answer 24

yeah there are no numbers you can plug in for x to get csc(x) = 0

Answer 25

okay :)

urmm, tan and cot? :/ I'm not quite sure i get what u mean.. sorry :(

Answer 26

No.
\[\huge \tan\frac\pi 2\]does not exist.
\[\huge \cot \frac \pi 2 = \frac{\cos \frac \pi 2}{\sin \frac \pi 2}\]

Answer 27

ohh :( darn... then idk :'(

Answer 28

So, since cos(pi/2) = 0, what does that mean for cot(pi/2) ?

Answer 29

cot(pi/2)=0 also?

Answer 30

Yes.
Since this graph is zero, at x = pi/2
then it might be either cosine or cotangent... which is it?
You know that the graph of cosine looks like a sine, IE, it is sinusoidal, IE it is wavy.... so your verdict?

Answer 31

verdict on like what i think the answer is?

Answer 32

Yes.

Answer 33

i still think it's D. y= cot x

is that right??

Answer 34

Yeah, it was correct, but I didn't want to make things too easy ^.^

Answer 35

haha yeah!! and thanks for the explanations :) i think i understand it a lot better now!! :D

Answer 36

Because the graph of cosine looks something like this