For what numbers theta is f(theta)=tan(theta) not defined? f(theta)=tan(theta) is not defined for numbers that are (even multiples, odd multiples, multiples) of (45, 90, 180*). Select an answer from each set of parentheses.

The numbers of theta that results to an undefined number for tan theta is odd multiples of pi/2. This means the answer to this problem is odd multiples of 90 degrees. you can try a calculator to find the answer since tan 90 is equal to 1/0 equal to infinity which is then undefined

Answer Link

lublana lublana · Answer 2 · 2019-07-22T02:33:43-04:00

Answer:

Hence, $tan\theta$ is not defined for odd multiples of $90^{\circ}$.

Step-by-step explanation:

We are given that $f(\theta)=tan(\theta)$

We have to find the value of theta for which$tan\theta$

We know that when $sin90^{\circ}=1$

and $cos90^{\circ}=0$

Then $tan90^{\circ}=\frac{sin90^{\circ}}{cos90^{\circ}}$

Substituting values

$tan90^{\circ}=\frac{1}{0}$

$tan90^{\circ}$ is not defined .

If we take

$\theta=45^{\circ}$

$tan45^{\circ}=\frac{1}{\sqrt3}$

Hence, $\tan\theta$is defined for odd multiples of$45^{\circ}$.

If we take $\theta= 180^{\circ}$

Then $tan180^{\circ}=\frac{sin180^{\circ}}{cos180^{\circ}}$

We know that $sin180^{\circ}=0\;and cos90^{\circ}=-1$

Therefore. $tan180^{\circ}=\frac{0}{-1}=0$

We know that 180 is even multiple of 90 and even multiple of 45 .Hence, we can say $tan\theta$ is no defined for odd multiples of 90

because$tan\frac{3\pi}{2}=tan(2\pi-\frac{\pi}{2})$

$=-tan\frac{\pi}{2}$

$=-tan90^{\circ}$

=not defined.

Hence, $tan\theta$ is not defined for odd multiples of $90^{\circ}$.