AmateurHour
contestada

Determined the quadrant for an angle with the following characteristics: cotθ>0 and cscθ>0.

A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV

Respuesta :

LammettHash
[tex]\csc\theta=\dfrac1{\sin\theta}>0\implies\sin\theta>0[/tex]

This happens whenever the terminal point of [tex]\theta[/tex] lies in either the first or second quadrants.

Meanwhile,

[tex]\cot\theta=\dfrac1{\tan\theta}=\dfrac{\cos\theta}{\sin\theta}>0\implies\cos\theta>0[/tex]

since you already know sine is positive. Cosine is positive when the angle lies in the first or fourth quadrant.

Sine and cosine are both positive only when [tex]\theta[/tex] is the first quadrant, which means this angle's terminal point lies in the first quadrant (A).

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