If sin θ < 0 and cos θ > 0, then the terminal point determined by θ is in:

realbrandon

If sin θ < 0 and cos θ > 0, then the terminal point determined by θ is in:

For some reason I am thinking its D. quadrant 4? (because It's the quadrant where y < 0 and x > 0, which is quadrant 4.) is this right?

topsquark

Forum Staff
If sin θ < 0 and cos θ > 0, then the terminal point determined by θ is in:

For some reason I am thinking its D. quadrant 4? (because It's the quadrant where y < 0 and x > 0, which is quadrant 4.) is this right?

No need to explain. You have it right.

-Dan

1 person

Soroban

MHF Hall of Honor
Hello, realbrandon!

Another approach . . .

$$\displaystyle \text{If }\sin\theta < 0\text{ and }\cos\theta > 0,\,\text{ then the terminal point determined by }\theta\text{ is in: }$$

. . $$\displaystyle \text{A. Quad 2} \qquad \text{B. Quad 1} \qquad \text{C. Quad 3} \qquad \text{D. Quad 4}$$

$$\displaystyle \sin\theta$$ is negative in Quad 3 and Quad 4.
$$\displaystyle \cos\theta$$ is positive in Quad 1 and Quad 4.

Therefore, $$\displaystyle \theta$$ is in Quad 4.