Question

How do I find csc (13pi/6) using the unit circle or calculator? Either way is fine.

Answer 1

13 PI / 6 is in radians and converting that to degrees we multiply it by 180 / PI which equals (13*30) = 390°

Answer 2

Thank you, but the answer sheet said the answer was 2. So how do I get that one, if you don't mind:) how. How should I be asking the question next time to get this sort of answer?

Answer 3

\[\Large\bf\sf \csc\left(\frac{13\pi}{6}\right)\quad=\quad \csc\left(\frac{12\pi}{6}+\frac{\pi}{6}\right)\quad=\quad \csc\left(2\pi+\frac{\pi}{6}\right)\]Since cosecant is periodic in 2pi,\[\Large\bf\sf \csc\left(2\pi+\frac{\pi}{6}\right)\quad=\quad \csc\left(\frac{\pi}{6}\right)\]They produce the same value. It's just a full spin around the circle back to the same spot. From there you'll want to remember your identity for cosecant.
\[\Large\bf\sf \csc(\pi/6)\quad=\quad \frac{1}{\sin(\pi/6)}\]pi/6 is one of our special angles and it gives us,\[\Large\bf\sf \csc(\pi/6)\quad=\quad \frac{1}{\left(\frac{1}{2}\right)}\]Dividing by a fraction, we can rewrite it as multiplication by flipping the term in the denominator,\[\Large\bf\sf 1\cdot\frac{2}{1}\quad=\quad 2\]

Answer 4

That's how you end up with 2. Hope that helps :)

Answer 5

Oh and I just noticed that this is your first question,
\(\Large\bf \color{#DD4747 }{\text{Welcome to OpenStudy! :)}}\)

Answer 6

Yes, I could have posted that as 30°
Rather than just posting the answer I figured I'd give d_everlasting a head start.

Answer 7

Thanks guys:)