Question

Determine the quadrant when the terminal side of the angle lies according to the following condition: cot (t) < 0, cos (t) < 0

Answer 1

Answer with explanation:

In first Quadrant, All trigonometric Ratios yields Positive value.

In Quadrant II,only Sine and Cosecant are Positive.

In Quadrant III, Tangent and Cotangent Function are Positive.

In Quadrant IV, Cosine and Secant are positive.

It is given that

Cotangent < 0

Cosine < 0

So, Only in Quadrant II, both Cotangent and Cosine of any Angle 't' is less than Zero.

⇒Terminal Side lies in Quadrant II.

Answer 2

cos(t)<0 (negative) it is negative when angle is in Quadrant 2. Or Quadrant 3
cot(t)<0. (negative) it is negative when angle lies in Quadrant 2 So,
the angle is in Q 2