Answer:
[tex]\tan(\theta) =[/tex] undefined
Step-by-step explanation:
Given
[tex]\sin(\theta) = -1[/tex]
Required
Determine [tex]\tan(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]
This gives:
[tex](-1)^2 + \cos^2(\theta) = 1[/tex]
[tex]1 + \cos^2(\theta) = 1[/tex]
Collect like terms
[tex]\cos^2(\theta) = 1 -1[/tex]
[tex]\cos^2(\theta) = 0[/tex]
Take square roots
[tex]\cos(\theta) = \sqrt 0[/tex]
[tex]\cos(\theta) = 0[/tex]
By tan identity
[tex]\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex]
[tex]\tan(\theta) = \frac{-1}{0}[/tex]
[tex]\tan(\theta) =[/tex] undefined
