Question

20 POINTS! ASAP PLS! Show work!!

Answer 1

QIV

Explanation:

To answer this question, we can use the standard ASTC acronym.

This stands for: All Students Take Calculus.

The first letter of each word tells us what is positive in each quadrant.

So, in QI, all trig ratios are positive.

In QII, only sine ( and cosecant) is positive.

In QIII, only tangent (and cotangent) is positive.

And in QIV, only cosine (and secant) is positive.

We know that csc(θ)<0. In other words, csc(θ) is negative.

Since csc(θ) is negative, sin(θ) is also negative.

So, our θ can't be in QI or QII.

We also know that sec(θ) is positive.

Our θ can only either be in QIII or QIV.

In QIII, only tangent is positive, so cosine will be negative.

So, θ is not in QIII.

So, the only choice that remains is QIV. And cosine and secant are indeed positive in QIV.

So, our angle θ is in QIV.

And we're done!

Answer 2

Hi there.

4th quadrant.

Recall that:

csc θ = 1 / (sin θ) - deals with y-values

sec θ = 1 / (cos θ) - deals with x-values

If csc θ < 0, then the y-coordinate of the angle must be negative.

If sec θ > 0, then the x-coordinate of the angle must be positive.

The quadrant on the coordinate plane that consists of negative y-coordinates and positive x-coordinates is the 4th quadrant.