Question

Refer to the table below if needed.

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

Read more about trigonometry ratios at:

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