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

Oct 2014
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2
Florida
If sin θ < 0 and cos θ > 0, then the terminal point determined by θ is in:

A. quadrant 2

B. quadrant 1

C. quadrant 3

D. quadrant 4

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?

Please explain answer. Thank you.
 

topsquark

Forum Staff
Jan 2006
11,578
3,454
Wellsville, NY
If sin θ < 0 and cos θ > 0, then the terminal point determined by θ is in:

A. quadrant 2

B. quadrant 1

C. quadrant 3

D. quadrant 4

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?

Please explain answer. Thank you.
No need to explain. You have it right.

-Dan
 
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Soroban

MHF Hall of Honor
May 2006
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6,341
Lexington, MA (USA)
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.