Respuesta :
tan ∅ and cot ∅
tan ∅ is undefined for ∅ = [tex]\frac{\pi }{2}[/tex]
and since cot ∅ = 1/ tan ∅ then cot ∅ is also undefined for ∅ = [tex]\frac{\pi }{2}[/tex]
Answer:
[tex]\tan\theta[/tex] is undefined when [tex]\theta=\frac{\pi}{2}[/tex] radians.
Step-by-step explanation:
Given : [tex]\theta=\frac{\pi}{2}[/tex] radians .
To find : Which function is undefined ?
Solution :
To check which functions are undefined put the value of [tex]\theta=\frac{\pi}{2}[/tex],
1) [tex]\cos\theta[/tex]
[tex]\cos\theta=\cos\frac{\pi}{2}=0[/tex]
2) [tex]\cot\theta[/tex]
[tex]\cot\theta=cot\frac{\pi}{2}[/tex]
[tex]\cot\theta=\frac{cos\frac{\pi}{2}}{sin\frac{\pi}{2}}[/tex]
[tex]\cot\theta=\frac{0}{1}[/tex]
[tex]\cot\theta=0[/tex]
3) [tex]\csc\theta[/tex]
[tex]\csc\theta=cosec\frac{\pi}{2}[/tex]
[tex]\csc\theta=\frac{1}{sin\frac{\pi}{2}}[/tex]
[tex]\csc\theta=\frac{1}{1}[/tex]
[tex]\csc\theta=1[/tex]
4)
[tex]\tan\theta=\tan\frac{\pi}{2}[/tex]
[tex]\tan\theta=\frac{sin\frac{\pi}{2}}{cos\frac{\pi}{2}}[/tex]
[tex]\tan\theta=\frac{1}{0}[/tex]
[tex]\tan\theta=\infity[/tex]
Therefore, [tex]\tan\theta[/tex] is undefined when [tex]\theta=\frac{\pi}{2}[/tex] radians.
