Question

what is the quadrant of $\theta$ if $\cos(\theta)$ is negative and $\sin(\theta)$ is positive?
show your work here
hint: to add the square root symbol ($\sqrt{\quad}$), type \sqrt\
\\(\circ i\\) \\(\circ i\\)
\\(\circ iii\\) \\(\circ iv\\)

Explanation:

Step1: Recall sign rules of trigonometric functions in each quadrant.

In Quadrant I: $\cos(\theta)>0$, $\sin(\theta)>0$.
In Quadrant II: $\cos(\theta)<0$, $\sin(\theta)>0$.
In Quadrant III: $\cos(\theta)<0$, $\sin(\theta)<0$.
In Quadrant IV: $\cos(\theta)>0$, $\sin(\theta)<0$.

Step2: Match the given conditions.

We know $\cos(\theta)$ is negative and $\sin(\theta)$ is positive. From the rules above, this matches Quadrant II.

Answer:

II (assuming one of the repeated "I" options was a typo and the intended options include II; if the original options have II, the answer is the option with II. Since the user's options seem to have a formatting error, but based on the analysis, the quadrant is II.)