Question

Please Help me!!!

Answer 1

what do you think about say \(\bf tan(\theta)
=\cfrac{{\color{brown}{ sin}}(\theta)}{{\color{blue}{ cos}}(\theta)}
\qquad

% cotangent
cot(\theta)
=\cfrac{{\color{blue}{ cos}}(\theta)}{{\color{brown}{ sin}}(\theta)}
\qquad


% secant
sec(\theta)

=\cfrac{1}{{\color{blue}{ cos}}(\theta)}\)

those 3, do their denominator ever become 0? if it does, then the fraction becomes undefined

Answer 2

and what about sin(x) ? does it ever become undefined?

Answer 3

So, if it lands on a zero, it becomes undefined and then it doesn't have all real numbers?

Answer 4

yeap

Answer 5

ok, thank you

Answer 6

if "x", turns into a number that makes the denominator 0, the fraction becomes undefined

and thus "x" CANNOT be that number, and thus then the function doesn't have all real numbers, because "x" is restricted there

Answer 7

whilst sin(x) has the luxury of pretty much have whatever value for "x"

Answer 8

So does this have all real numbers? because in the middle it lands on zero

Answer 9

sure, \(\Large \mathbb{R}\quad means\quad (+\infty, -\infty)\)

Answer 10

keep in mind we're referring to the x-axis, NOT the range, or y-axis
the y-axis is clearly constrained, but that's the range

Answer 11

what about this one?