Question

Help Please?! Medal

Answer 1

@TheSmartOne @jim_thompson5910 @SolomonZelman

Answer 2

@TheSmartOne @Mertsj @jim_thompson5910

Answer 3

Factor out tan(x)

Answer 4

Oh, thanks! I'll try that

Answer 5

yw

Answer 6

@Mertsj I'm stuck.
I got this:
tan x (sec x -2) = 0
tan x = 0
x = 0

sec x - 2 = 0
sec x = 2

?

Answer 7

I don't know anything about this :/ Sorry..

Answer 8

\[\tan(x)=0 \\ \cos(x)=\frac{1}{2}\]

Answer 9

are the equations you have to solve

Answer 10

if \(\sec(x)=2\) then \(\cos(x)=\frac{1}{2}\)

Answer 11

and actually we can just say solve sin(x)=0 and solve cos(x)=1/2

Answer 12

all your choices have \[0+k\pi\] from the \(\tan(x)=0\)

Answer 13

oh, right. thanks. don't know where my brain is

Answer 14

Correction: \[\tan(x) = 0 \implies x =\tan^{-1}(0)\]

Answer 15

x = 60 then...which is pi/3 in radians

Answer 16

also your choices are weird

Answer 17

You had written \[\tan(x) = 0\]\[x=0\]

Answer 18

Would the answer be B or D?

Answer 19

none of your choices make any sense
one of your choices are close

Answer 20

but it is still not correct

Answer 21

Ok first off, what is the first value when \(x =\tan^{-1}(0)\)?

Answer 22

0 ^

Answer 23

And what are your domain restrictions? \([0,2\pi)\)?

Answer 24

I don't think there are any? ^

Answer 25

If tan x = 0 then x is 0 or pi
If sec x = 2 then cos x = 1/2 and x = pi/3 or 5pi/3

Answer 26

This all makes some sense to me, bu none of it is in the answer choices...ugh

Answer 27

hint:
cos(x) is even
so you could say cos(x)=cos(-x)
but none of your choices will work

Answer 28

because k can't be irrational and an integer at the same time

Answer 29

Yes, there is a correct answer choice in that bunch

Answer 30

since x = pi/3, would x also work for any value that was (pi k)/3 ???

Answer 31

k equaling 1, 2, 3 , etc?

Answer 32

you're on the right track.

Answer 33

That's why I was thinking B or D ^

Answer 34

there is not a correct choice ...

Answer 35

You know, only one of the given solutions actually make sense.

Answer 36

D? ^

Answer 37

Well, if you think it is D, then plug in values for k that satisfy both x = 0 and x = 1/2

Answer 38

For example first option has \(2k+\pi/3\).

Answer 39

2kpi+pi/3

Answer 40

should be that ^

Answer 41

No way \(2k\) makes any sense.

Answer 42

@Jhannybean I plugged in 1 for k + pi/3, and it worked. I got 0

Answer 43

:)

Answer 44

a lot of the thingys are missing pi

Answer 45

Thanks @Jhannybean

Answer 46

Keep going @StudyGurl14

Answer 47

Wait a minute, do you understand, @freckles ?

Answer 48

If not, explain @StudyGurl14 :)

Answer 49

Yes I been saying done of these choices are correct... lol.
but one of them is kinda close.

Answer 50

none*

Answer 51

Wait @Jhannybean It can't be D...cause I plugged in 2 for k, and it didn't work. it didn't result in 0

Answer 52

wait, hold on i made a mistake

Answer 53

But you have two conditions to satisfy, do you not?

Answer 54

It's not D, I don't think...

Answer 55

I'm back to thinking it is B, but even that doesn't work right...*sigh*

Answer 56

this is what I'm saying...
the choices should look like this:
\[A) 0+\pi k , 2k \pi+\frac{\pi}{3}, 2k \pi-\frac{\pi}{3} \\ B)0+\pi k, \frac{\pi k}{3}, \frac{2 \pi k}{3} \\ C) 0+ \pi k, 2k \pi+\frac{\pi}{3}, k \pi+\frac{2\pi}{3} \\ D) 0+\pi k , k \pi +\frac{\pi}{3}, k \pi +\frac{2\pi}{3}\]

Answer 57

I don't think so @freckles ...

Answer 58

Why would they need two pi's?

Answer 59

If tan x = 0 then x is 0 or pi
\[0^{o}+\pi k\]

Answer 60

If sec x = 2 then cos x = 1/2 and x = pi/3 or 5pi/3

Answer 61

pi/3+2pi*k
this explains all the angles that end up at that one particular coordinate (1/2, sqrt(3)/2)
this tells us that
the following are solutions
pi/3
pi/3+2pi
pi/3+4pi
and so on...
if we go pi/3 and then 2pi/3 we land at the same location we stopped at before

Answer 62

x=pi/3
\[\frac{\pi}{3} +2k \pi \]

Answer 63

pi/3+2 makes no sense at all

Answer 64

Okay, so I used mathway, and it says this:

Answer 65

5pi/3 is the same as - pi/3

Answer 66

BUT, that's not an answer choice....*sigh*

Answer 67

oops /3 was a type-o

Answer 68

So choose the first answer and be done with it already

Answer 69

cos(x)=cos(-x)
so if pi/3 is a solution then -pi/3 is also a solution

Answer 70

but i would still say none of these and put the write solution :p

Answer 71

right

Answer 72

That's what @Mertsj is saying,

Answer 73

OH! So then A

Answer 74

but it really isn't A

Answer 75

but A is the closest

Answer 76

I see. Thanks.

Answer 77

\[2\pi n+\frac{\pi}{3} , 2 \pi n+\frac{-\pi}{3}\]

Answer 78

It was A...man if that was the practice test, I'm afraid of the real thing...haha

Answer 79

hopefully there won't be any type-os :p

Answer 80

yeah...stupid Connections Academy...

Answer 81

If it was a real test, then you'd have to tell a teacher that the answers are wrong.