Question

Use the unit circle to determine the value of sec(-12pi)

Answer 1

to make it easy
add 2pi into -12pi ntill you get positive value
and remember sec =1/cos

Answer 2

i still dont get it

Answer 3

add 2pi \[\huge\rm -12\pi +2\pi\]
full circle is equal to 2pi that's why we have to add 2pi
keep adding 2 untill u get positive number

Answer 4

\[-12\pi +2\pi = -10 \]
still negative add 2pi again
\[-10\pi +2\pi = -8\pi \]
add 2pi again

Answer 5

ok i get 0pi

Answer 6

so it is not an exact value then

Answer 7

\[-12\pi +2\pi = -10 \]
still negative add 2pi again
\[-10\pi +2\pi = -8\pi \]
add 2pi again
\[-8\pi +2\pi = -6\pi \]
add 2pi
\[-6\pi +2\pi = -4\pi \]
\[-4\pi +2\pi = -2\pi \]
add 2 pi again and let me know what you get

Answer 8

i get 0pi

Answer 9

okay 0 is correct

Answer 10

not pi just 0

Answer 11

so it is undefined

Answer 12

like i told you
sec =1/cos
look at the unit cricle what is cos at 0

Answer 13

cos(0)=1

Answer 14

yep right so \[\huge\rm sec =\frac{1}{cos} =sec =\frac{ 1 }{ 1 }\]
replace cos by 1 = answer

Answer 15

don't forget the *one* at the numerator !

Answer 16

if the answer is 0 the is it undefined or not

Answer 17

no

Answer 18

they are asking for value of sec(-12pi) in the unit circle
radians is 0 to 2pi(-12pi is not in the unit circle t decrease the value we added 2pi )
degree 0 to 360

Answer 19

so in other words question is find the value fo sec(0)

Answer 20

sec(0) is same as sec(-12pi) both are equal

Answer 21

no i am just asking in general, does the answer 0 mean undefined

Answer 22

ohh okay no
well if the DENOMINATOR is 0 then YES!! answer is undefined

Answer 23

okay here is an example let's say they are asking csc(0)
and csc equal to 1/sin and now sin (0) is 0
right

Answer 24

so when you replace sin by 0 your answer would be undefined because there is a zero at the denominator \[\large \rm csc = \frac{ 1}{\sin} = \frac{ 1 }{ 0 }=\rm undefined\]

Answer 25

\[\huge\rm \frac{ 1 }{ 0 }= undefined ~~~~~~~~~~~~~\frac{ 0 }{ 1}=1\]
and just simple 0 doesn't mean undefined