Question

Help explaining how to find the domain of tangent functions

Answer 1

so the domain of a tangent is all real number except odd multiples of \[\frac{ \pi }{ 2b }+\frac{ c }{ b }\]

Answer 2

The characteristic of a tangent function is \[f(\theta)=atan(b \theta-c)+d\]

Answer 3

so with this how would you do that with \[f(\theta)=\tan(1/2 \pi \theta)-2\]

Answer 4

would pi be b?

Answer 5

b is the "stuff" in front of theta
I can't tell if it's 1/(2pi) or pi/2 . but whatever it is, that is b
once you know b, you use it in the very first post

Answer 6

@phi sorry its tan(1/2)pi theta)

Answer 7

so c would be 1/2 then so \[\frac{ \pi }{ 2\pi }+\frac{ \frac{ 1 }{ 2 } }{ \pi }\]

Answer 8

if it's
\[ \tan\left(\frac{1}{2} \pi \theta \right) -2\]
that is the same as
\[ \tan\left(\frac{\pi}{2} \theta \right) -2\]

Answer 9

Why would that be exactly I am confused :/

Answer 10

and also if it is pi/2 then what would be c? 0?

Answer 11

the site is being a pain. anyway,
we match up
\[ \tan\left(\frac{\pi}{2} \theta \right) -2 \]
with \[ f(\theta)=\tan(b \theta-c)+d \]
there is no "c" (c is 0)
b is pi/2

so we use those in
\[ \frac{ \pi }{ 2b }+\frac{ c }{ b } \]

we need 2*b, which is 2*pi/2 = pi
and put that in your formula:
\[ \frac{ \pi }{ \pi }+\frac{ 0 }{ b } \]
it looks like we get 1

Answer 12

so it is all real numbers except odd multiples of 1?

Answer 13

the domain of a tangent is all real number except odd multiples
of 1
I guess that would be all numbers except 1,3,5,... (the odd numbers)

Answer 14

so except odd integers

Answer 15

yes

Answer 16

Thank you so much for your help. I kinda have just been trying to solve this for like 3 hours now s: so this should help me solve the other ones. I cannot thank you enough

Answer 17

so one more thing I was doing the next one which is \[f(\theta)=\tan(\frac{ 1 }{ 3 }\pi \theta)+1 \]
Which would be \[\tan(\frac{ \pi \theta }{ 3 })+1\]
so if you put this into the equation
so this would be 3/2+0/pi
@phi would the final answer be All real numbers except for the odd multiples of 3/2?

Answer 18

I believe this is right so :P you explaining did help me alot ahaha