cos^-1(0) is the angle(s)for which the cosine is zero.
pi/2 (radians) is one such angle.
So is 3 pi/2. There are others at multiples of pi.
There are no real values of x for which cos x is undefined.
ok I was doing this problem
cos^-1 (0)
and was like oh that would be pi/2 but then I thought about it some and decided that even though it's right it can't possibly be...
if tan(pi/2) = the first derrivative of a vertical line = undefined
well not really there's a deffintion correct it has a value... a number that approaches zero (from both directions?)... wow uh?... but is not zero becasue the line exists and in order for it to be in existence... there is a first derrivative... right so it's not that it doesn't exist... just not defined... there's a value... that I could find some way to define would... uh... hm....
but ya anways so I thoguht about that and was like so then why on earth do we define cosine of a vertical line (pi/2) to be zero... it's not zero because it's in existence just incredably small... aproaches zero from both sides... interesting... just like tangent shouldn't then have some true value that's not zero that we should leave undefined...
I know i know... by defintion it's zero put in your calculator... ya but if you think about it it's not really zero is it it's really undefined...
unless those are two different versions of undefined??
the width of a vertical line that has no width... but exists so therefore has one just like the first derrivative of it...
well I'm confused... can you please help me understand as just thinking about it leads me to believe that cosine pi/2 is really undefined just like tangent pi/2 is... why is it not undefined shouldn't be... why do we say it's zero casue it's really not now is it...???
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