Value of cosec

**scofield131** · November 8th 2009, 08:07 AM

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?

**e^(i*pi)** · November 8th 2009, 08:14 AM

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 $\frac{2}{3}$

**scofield131** · November 8th 2009, 08:19 AM

That makes sense. Thanks :]

**pencil09** · November 8th 2009, 08:32 AM

sorry double post....

**pencil09** · November 8th 2009, 08:36 AM

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 $\frac {1}{\left(\frac{\sqrt3}{2}\right)^2} =\left (\frac{2}{\sqrt3}\right)^2 =\frac{4}{3}$

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