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

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

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

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\[-12\pi +2\pi = -10 \] still negative add 2pi again \[-10\pi +2\pi = -8\pi \] add 2pi again
ok i get 0pi
so it is not an exact value then
\[-12\pi +2\pi = -10 \] 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
i get 0pi
okay 0 is correct
not pi just 0
so it is undefined
like i told you sec =1/cos look at the unit cricle what is cos at 0
cos(0)=1
yep right so \[\huge\rm sec =\frac{1}{cos} =sec =\frac{ 1 }{ 1 }\] replace cos by 1 = answer
don't forget the *one* at the numerator !
if the answer is 0 the is it undefined or not
no
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
so in other words question is find the value fo sec(0)
sec(0) is same as sec(-12pi) both are equal
no i am just asking in general, does the answer 0 mean undefined
ohh okay no well if the DENOMINATOR is 0 then YES!! answer is undefined
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
so when you replace sin by 0 your answer would be undefined because there is a zero at the denominator \[\large \rm csc = \frac{ 1}{\sin} = \frac{ 1 }{ 0 }=\rm undefined\]
\[\huge\rm \frac{ 1 }{ 0 }= undefined ~~~~~~~~~~~~~\frac{ 0 }{ 1}=1\] and just simple 0 doesn't mean undefined

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