Respuesta :
Answer:
Option 4 [tex]tan\theta[/tex] is undefined.
Step-by-step explanation:
Given : [tex]\theta=\frac{\pi}{2}[/tex] radians
To find : Which function is undefined
Solution : Put [tex]\theta=\frac{\pi}{2}[/tex] in all the given options to check which are undefined
[tex]Cos\theta=cos\frac{\pi}{2}=0[/tex]
[tex]Cot\theta=cot\frac{\pi}{2}=\frac{cos\frac{\pi}{2}}{sin\frac{\pi}{2}}=\frac{0}{1}=0[/tex]
[tex]Csc\theta=cosec\frac{\pi}{2}=\frac{1}{sin\frac{\pi}{2}}=\frac{1}{1}=1[/tex]
[tex]tan\theta=tan\frac{\pi}{2}=\frac{sin\frac{\pi}{2}}{cos\frac{\pi}{2}}=\frac{1}{0}=infinity[/tex]
Therefore, we get that[tex]tan\theta[/tex] is not defined or undefined.
For cos [tex]\theta =0[/tex], [tex]\rm \theta[/tex] will be [tex]\pi/2[/tex] and tan [tex]\theta[/tex] will not be defined. Thus, for n = 0, [tex]\theta[/tex] becomes [tex]\pi[/tex]\2, [tex]\rm tan\ \theta[/tex] is not defined.
What is a trigonometric function?
These are also known as circular functions can be defined as the function of the angle of the triangle. The circular function is the function that repeats itself after a regular interval of time is called the CIrcular function or trigonometric function.
Given
[tex]\rm \theta= \dfrac{\pi}{2}[/tex]
To find
The function is undefined when [tex]\rm \theta= \dfrac{\pi}{2}[/tex].
How to get the trigonometric function is undefined at [tex]\pi[/tex]/2?
[tex]\rm cos\ \theta[/tex] is defined for all the values of [tex]\theta[/tex].
[tex]\rm cot\ \theta[/tex] is defined for all the values except [tex]n\pi[/tex].
[tex]\rm cosec\ \theta[/tex] is defined for all the values except [tex]n\pi[/tex].
[tex]\rm tan\ \theta[/tex] is defined for all the values except [tex]n\pi \pm \dfrac{\pi }{2}[/tex].
Thus, for n = 0, [tex]\theta[/tex] becomes [tex]\pi[/tex]\2, [tex]\rm tan\ \theta[/tex] is not defined.
More about the Trigonometric function link is given below.
https://brainly.com/question/6904750
