Answer:
Hence, [tex]tan\theta[/tex] is not defined for odd multiples of [tex]90^{\circ}[/tex].
Step-by-step explanation:
We are given that [tex]f(\theta)=tan(\theta)[/tex]
We have to find the value of theta for which[tex]tan\theta[/tex]
We know that when [tex]sin90^{\circ}=1[/tex]
and [tex]cos90^{\circ}=0[/tex]
Then [tex]tan90^{\circ}=\frac{sin90^{\circ}}{cos90^{\circ}}[/tex]
Substituting values
[tex]tan90^{\circ}=\frac{1}{0}[/tex]
[tex]tan90^{\circ}[/tex] is not defined .
If we take
[tex]\theta=45^{\circ}[/tex]
[tex]tan45^{\circ}=\frac{1}{\sqrt3}[/tex]
Hence, [tex]\tan\theta[/tex]is defined for odd multiples of[tex]45^{\circ}[/tex].
If we take [tex]\theta= 180^{\circ}[/tex]
Then [tex]tan180^{\circ}=\frac{sin180^{\circ}}{cos180^{\circ}}[/tex]
We know that [tex]sin180^{\circ}=0\;and cos90^{\circ}=-1[/tex]
Therefore. [tex]tan180^{\circ}=\frac{0}{-1}=0[/tex]
We know that 180 is even multiple of 90 and even multiple of 45 .Hence, we can say [tex]tan\theta[/tex] is no defined for odd multiples of 90
because[tex] tan\frac{3\pi}{2}=tan(2\pi-\frac{\pi}{2})[/tex]
[tex]=-tan\frac{\pi}{2}[/tex]
[tex]=-tan90^{\circ}[/tex]
=not defined.
Hence, [tex]tan\theta[/tex] is not defined for odd multiples of [tex]90^{\circ}[/tex].
