Thread: Value of cosec

1. Value of cosec

Excuse the silliness of this question. It's been a wee while since I've done maths and I think I've forgotten something really basic.

Anyway, I've got to find the value of y= - cosec^2(pi.x) where x = 1/3

So far, I've gotten down to:

= - 1/sin(60)

Which, when banged into the calculator, = 1/ (square root)3/2 [if that makes sense].

But, I'm conscious of the squared sign in the cosec. Does that mean anything?

2. Originally Posted by scofield131
Excuse the silliness of this question. It's been a wee while since I've done maths and I think I've forgotten something really basic.

Anyway, I've got to find the value of y= - cosec^2(pi.x) where x = 1/3

So far, I've gotten down to:

= - 1/sin(60)

Which, when banged into the calculator, = 1/ (square root)3/2 [if that makes sense].

But, I'm conscious of the squared sign in the cosec. Does that mean anything?
$cosec^2(\pi \, x) = \frac{1}{sin^2(\pi \, x)}$

As you rightly mentioned $sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

Therefore it becomes $\frac{1}{\left(\frac{\sqrt3}{2}\right)^2}$

I got an overall answer of $\frac{2}{3}$

3. That makes sense. Thanks :]

4. sorry double post....

5. Originally Posted by e^(i*pi)
$cosec^2(\pi \, x) = \frac{1}{sin^2(\pi \, x)}$

As you rightly mentioned $sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

Therefore it becomes $\frac{1}{\left(\frac{\sqrt3}{2}\right)^2}$

I got an overall answer of $\frac{2}{3}$

the last one (result), i think it should be $\frac{4}{3}$
since $\frac {1}{\left(\frac{\sqrt3}{2}\right)^2} =\left (\frac{2}{\sqrt3}\right)^2 =\frac{4}{3}$