Question

Which function is undefined when x= pi/2 radians cos x cot x csc x tan x

Answer 1

Answer:

Option 4 that is tan x will be undefined at x=pi/2 radians

Step-by-step explanation:

$\frac{\pi}{2}radians=90^{\circ}$

In case 1:

We have cos x

$\text{Cos x has value 0 at x}=\frac{\pi}{2}radians$

Therefore the function is defined hence, option 1 is discarded.

In case 2:

We have cot x and

$cot x=\frac{cos x}{sin x}$

Since, $\text{cos x at x}=\frac{\pi}{2}\text{radians is 0}$

And $\text{sin x at x}=\frac{\pi}{2}\text{radians is 1}$

Hence,$cot x=\frac{0}{1}=0$

Hence, defined and Option 2 is discarded.

In case 3:

We have csc x and

$csc x=\frac{1}{sin x}$

Since, $\text{sin x at x}=\frac{\pi}{2}\text{radians is 1}$

Hence,$csc x=\frac{1}{1}=1$

Hence, defined and Option 3 is discarded.

In case 4:

We have tan x and

$tan x=\frac{sin x}{cos x}$

Since, $\text{cos x at x}=\frac{\pi}{2}\text{radians is 0}$

And $\text{sin x at x}=\frac{\pi}{2}\text{radians is 1}$

Hence,$tan x=\frac{1}{0}=\infty$

Hence, undefined and Option 4 is correct.

Answer 2

The Cot x is undefined because it is equal to (Sin x)/(Cos x) and at pi/2, Cosine = 0.