Question

Refer to the table below if needed.
Second Quadrant
Third Quadrant
Fourth Quadrant
sin(1800-e) = sine
sin(1800 +) = -sino
sin(3600-0) = - sino
cos(180°-2) = - COS
cos(1800 +) = - COS
cos(360°-) = cos
tan(180°-2) = - tane
tan(180° +2) = tano
tan(360°-O) = - tane
cot(1800-0) = -coto
cot(180° +0) = cote
cot(3600-0) = - coto
sec(180° +2) = - Seco
sec(360° -2) = seco
sec(180°-o) = - Seco
csc(180° -2) = CSCO
CSC(180° +) = - CSCO
CSC(3600-0) = - CSCO
The quadrants in which tane and cote are positive.
IV

Answer 1

A quadrant is the area that is divided into the x and y axes

The quadrants in which tan $\theta$ and cot $\theta$ are positive are I and III

How to determine the quadrants

The tangent of an angle is calculated as:

$\tan(\theta) = \frac{sin(\theta)}{\cos(\theta)}$

While the cotangent of the angle is calculated as:

$\cot(\theta) = \frac{cos(\theta)}{\sin(\theta)}$

The above equations mean that:

For the tangent and cotangent of an angle to be positive, then the sine and the cosine of the angle must have the same sign.

• In the first quadrant, the sine and the cosine angles are positive.
• In the third quadrant, the sine and the cosine angles are negative.

Hence, the quadrants in which tan $\theta$ and cot $\theta$ are positive are I and III

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