DETERMINE THE QUADRANT IN WHICH THE TERMINAL SIDE LIES

Question :

For each description, in which quadrant does the terminal arm of angle θ lie?

a) cos θ < 0 and sin θ > 0

b) cos θ > 0 and tan θ > 0

c) sin θ < 0 and cos θ < 0

d) tan θ < 0 and cos θ > 0

Solution : 

(a)  cos θ < 0 and sin θ > 0

According to the given information, we know sin θ will have positive sign and that cos θ will have negative sign.

Remembering ASTC formula, the terminal arm lies in 2nd quadrant.

(b) cos θ > 0 and tan θ > 0

Solution :

According to the given information, we know cos θ and tan θ will have positive sign.

Remembering ASTC formula, the terminal arm lies in 1st quadrant.

(c) sin θ < 0 and cos θ < 0

Solution :

According to the given information, we know both sin θ cos θ will have negative sign.

In ASTC formula T stands for third quadrant. In that other than tan θ and cot θ for other trigonometric ratios, we will have negative sign.

Hence the terminal arm lies in 3rd quadrant.

(d) tan θ < 0 and cos θ > 0

Solution :

According to the given information, we know cos θ will have positive sign and tan θ will have negative sign.

Remembering ASTC formula, the terminal arm lies in 4th  quadrant.

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