Question

Will give medal!
How can you tell when an expression is undefined?
Some examples:
sec (-pi/2)
csc (3*pi)
cot (7*pi/2)
csc (-3*pi/2)
cot (5*i/3)

Answer 1

so.... when is a fraction undefined?

Answer 2

when zero is the denominator, but I don't see how you can tell that in this situation. I've tried typing them all into a calculator, but that doesn't help.

Answer 3

When the denominator is 0.

Answer 4

Remember that pi=180. You need to simplify.

Answer 5

I thought pi was equal to 3.14 rounded?

Sorry for the late response. I was looking at another question.

Answer 6

hmm yes when the denominator is 0
so

Answer 7

So pi = 180 when the denominator equals 0?

Answer 8

one sec

Answer 9

okay

Answer 10

\(\bf sec\left(-\frac{\pi}{2}\right)\implies \cfrac{1}{{\color{brown}{ cos}}\left(-\frac{\pi}{2}\right)}\implies \cfrac{1}{{\color{brown}{ cos}}\left(\frac{\pi}{2}\right)}
\\ \quad \\
csc\left(\frac{3\pi}{2}\right)\implies \cfrac{1}{{\color{brown}{ sin}}\left(\frac{3\pi}{2}\right)}
\\ \quad \\
cot\left(\frac{7\pi}{2}\right)\implies \cfrac{cos\left(\frac{7\pi}{2}\right)}{{\color{brown}{ sin}}\left(\frac{7\pi}{2}\right)}
\\ \quad \\
csc\left(-\frac{3\pi}{2}\right)\implies \cfrac{1}{{\color{brown}{ sin}}\left(-\frac{3\pi}{2}\right)}\implies \cfrac{1}{{\color{brown}{ -sin}}\left(\frac{3\pi}{2}\right)}\)

so.. if you find the value of the function in the denominator.. and if it zeros out....then the fraction will be undefined, and so will the trig function

Answer 11

and the last one, the cotangent one, is the same as that one above
just change it to cosine and sine based
and check if at that angle the denominator zeros out

Answer 12

So cot (3*pi/2) would be undefined since it cancels out?

Answer 13

you mean csc?

Answer 14

yeah sorry csc

Answer 15

\(\bf csc\left(\frac{3\pi}{2}\right)\implies \cfrac{1}{{\color{brown}{ sin}}\left(\frac{3\pi}{2}\right)}\implies \cfrac{1}{-\cancel{ 1 }}\to -1\)

Answer 16

anyhow they cancel out.. but \(\bf \cfrac{\cancel{ 1 }}{-\cancel{ 1 }}\to -1
\)

Answer 17

one of the ones that's simple will be say the 1st one \(\bf sec\left(-\frac{\pi}{2}\right)\implies \cfrac{1}{{\color{brown}{ cos}}\left(-\frac{\pi}{2}\right)}\implies \cfrac{1}{{\color{brown}{ cos}}\left(\frac{\pi}{2}\right)}\to \cfrac{1}{0}
\)

Answer 18

When I typed them into the calculator
cos(pi*2) = 0
cos(7*pi/2)/sine(7*pi/2) = 0

Answer 19

and based off what you said earlier that means that cot (5*i/3) = 0 as well correct?

Answer 20

My assignment says that:
sec(-pi/2) and csc(3*pi) are the only undefined expressions. Could you tell me where I went wrong?

Answer 21

well... \(\bf cot\left(\frac{5\pi}{3}\right)\implies \cfrac{cos\left(\frac{5\pi}{3}\right)}{sin\left(\frac{5\pi}{3}\right)}\to \cfrac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}\to \cfrac{1}{\cancel{ 2 }}\cdot -\cfrac{\cancel{ 2 }}{\sqrt{3}}\)

Answer 22

Ah I see now.
but how does cot (7*pi/2) not equal zero?

Answer 23

ok well keep in mind that \(\bf \cfrac{7}{2}\to \cfrac{6}{2}+\cfrac{1}{2}\to 3+\cfrac{1}{2}\) so one can say that \(\bf \cfrac{7\pi}{2}\to \cfrac{6\pi}{2}+\cfrac{\pi}{2}\to 3\pi+\cfrac{\pi}{2}\)

so. where's that angle anyway? well
is 3 go-round or full cycles and then \(+\cfrac{\pi}{2}\)

so