How do I compute this on a calculator?

Question

anonymous · Answer

$$\csc(x) = 20$$

hba · Answer

Do you want to calculate X @MrFrizzy

anonymous · Answer

x= -15

anonymous · Answer

I am looking for all solutions between -pi and pi
In radians as well

anonymous · Answer

I know the answers are really close to -pi and pi, but I don't know how to compute it on a calculator

zepdrix · Answer

$$\large \csc x = \frac{1}{\sin x}$$
$$\large \csc x =20 \qquad \rightarrow \qquad \frac{1}{\sin x}=20$$Then do some math to solve for sin x.$$\large \sin x = \frac{1}{20}$$

Now depending on whether you want your answer in radians or degrees, adjust the mode accordingly.

We can rewrite this function as the inverse trig function by switching the argument with the other term, like so,$$\large \sin^{-1}\left(\frac{1}{20}\right)=x$$
So you'll need to find this button on your calculator :)

zepdrix · Answer

Hmm it doesn't appear to be near -pi or pi, it appears to be really really close to 0 actually :o

anonymous · Answer

So then the two answers are .0500 and pi-.0500

zepdrix · Answer

Mmmm yah that's prolly right :) I know the 0.0500 is correct. I always forget how to find the second angle lol.

anonymous · Answer

Should be pi minus the first answer since the parabola is symmetrical on each side. The left side is .0500 from the asymptote therefore it should be .0500 from the right hand side asymptote