Question

WILL GIVE BRAINLIEST.

Answer 1

Answer:

$\tan(\theta) =$ undefined

Step-by-step explanation:

Given

$\sin(\theta) = -1$

Required

Determine $\tan(\theta)$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$(-1)^2 + \cos^2(\theta) = 1$

$1 + \cos^2(\theta) = 1$

Collect like terms

$\cos^2(\theta) = 1 -1$

$\cos^2(\theta) = 0$

Take square roots

$\cos(\theta) = \sqrt 0$

$\cos(\theta) = 0$

By tan identity

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

$\tan(\theta) = \frac{-1}{0}$

$\tan(\theta) =$ undefined