Video 24: Graphing basic tangent functions
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couldnt you have simply said domain = all real numbers not equal to 0
TENNSUMITSUMA 5 months ago
@TENNSUMITSUMA No -- zero is allowed, so it is part of the domain. What is NOT part of the domain is 90 degrees. Also, -90 degrees is not allowed. And 180 degrees is also not allowed. That's why the domain is {x|x is not equal to 90 degrees +k} where k is an integer. Look at the video at 3:36 to see all the points where x is not allowed. (The video uses radians, so it is given as pi/2 instead of 90 degrees, but they are equivalent.)
dyagodich in reply to TENNSUMITSUMA (Show the comment) 5 months ago
@dyagodich
i dont get it, if 'k' is integer
arent you saying that you cant use any number? i dont get where k or 'k pi' comes in. and why cant you use 180? its 0/1 so there is a domain.
TENNSUMITSUMA in reply to dyagodich (Show the comment) 5 months ago
You can use any number for k. I made a mistake in my comment above-x cannot equal 90+180k (not 90+k).
If k=0, 90+ 0=90. So x cannot equal 90
If k=1, 90+1*180=180. So x cannot equal 270
If k=-1, 90+(-1)*180=-90. So x cannot equal -90
You can pick any integer for k. I cannot plug x=-90 or x=90 or x= 270 or x=90+180*k into tan(x). The reason is 180 (or pi) is the period of tangent, not 2pi like sin or cos. (But 180 is okay. I can't pick a k to make 90+180k=180,so it is allowed)
dyagodich in reply to TENNSUMITSUMA (Show the comment) 5 months ago
@dyagodich
i didnt get any of that.
i dont get what k is supposed to be
i dont get why you cant use 180 since there wouldnt be a 0 in the denominator like with 90 and 270.
i keep watching the vids but im not getting it.
why is it 90+ ...., how come it always starts with 90
TENNSUMITSUMA in reply to dyagodich (Show the comment) 5 months ago
The question is -- what is the domain of tangent. That is, what am I allowed to use for x. Sine and cosine have no limits on what I can use for x. But tangent does. Try using your calculator (in degree mode) and find "tan(0)". That's find -- tan(0) is just 0. But try typing in tan(90). You'll get "Err:Domain". That is, x CANNOT equal 90 degrees. As I said in my previous comment, tan(180) *is* fine. It is also zero. But tan(270) also gives an error. ANY multiple of 90 doesn't work.
dyagodich in reply to TENNSUMITSUMA (Show the comment) 5 months ago