Answer:
QII
Step-by-step explanation:
We can use the acronym: ASTC or All Students Take Calculus.
The first letter of each word tells us details within a certain quadrant.
All trig functions in QI will be positive.
Only sine (and cosecant) will be positive in QII.
Only tangent (and cotangent) will be positive in QIII.
And only cosine (or secant) will be positive in QIV.
We know that tan(θ)<0. In other words, it's negative.
So, it our angle θ <em>cannot</em> be in QI or QIII.
We also know that cos(θ)<0.
So, this removes QIV, since in QIV, cosine is positive.
Therefore, the only choices that remains is QII.
In QII, sine is positive, tangent is negative, and cosine is negative.
This fits all our conditions, so θ is in QII.
And we're done!
