DETERMINE THE QUADRANT IN WHICH THE TERMINAL SIDE LIES

Determine the Quadrant in Which the Terminal Side Lies

Here we are going to see how to determine the quadrant in which the terminal sides lies.

Question 1 :

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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