Which of the following best represents the graph of f(x)= tan ( sin x), x ≥ 0 ?

Question

Which of the following best represents the graph of f(x)= tan ( sin x), x ≥ 0 ? (A)  (B)  (C)  (D) ****

Tardigrade Admin · Accepted Answer

f ( x )= tan ( sin x) is an odd function on (-∞, ∞). Range of f(x)=[- tan 1, tan 1]. Also, f(x) is continuous and differentiable for all x ∈ R Note that, tan 1>1 and - tan 1<-1. Also, f ( x ) is periodic with fundamental period 2 π.

Q. Which of the following best represents the graph of $f (x) = tan (sin x), x \geq 0$ ?

****

$f (x) = tan (sin x)$ is an odd function on $(- \infty, \infty)$ .
Range of $f (x) = [- tan 1, tan 1]$ .
Also, $f (x)$ is continuous and differentiable for all $x \in R$
Note that, $tan 1 > 1$ and $- tan 1 < - 1$ .
Also, $f (x)$ is periodic with fundamental period $2 π$ .

Q. Which of the following best represents the graph of f(x)=tan(sinx),x≥0 ?

****

f(x)=tan(sinx) is an odd function on (−∞,∞). Range of f(x)=[−tan1,tan1]. Also, f(x) is continuous and differentiable for all x∈R Note that, tan1>1 and −tan1<−1. Also, f(x) is periodic with fundamental period 2π.

Q. Which of the following best represents the graph of $f (x) = tan (sin x), x \geq 0$ ?

$f (x) = tan (sin x)$ is an odd function on $(- \infty, \infty)$ .
Range of $f (x) = [- tan 1, tan 1]$ .
Also, $f (x)$ is continuous and differentiable for all $x \in R$
Note that, $tan 1 > 1$ and $- tan 1 < - 1$ .
Also, $f (x)$ is periodic with fundamental period $2 π$ .