Question

Tangent is positive in quadrants i and iv only. (True/False)

Answer 1

False, Tangent is only positive in quadrants I and III.

Explanation:

Tangent of a measurement, or tanθ, can equal the ratio of sinθ to cosθ. This can be mathematically expressed as:

`\displaystyle{\tan \theta = (\sin \theta)/(\cos \theta)}`

We know that in order for tanθ to be positive. sinθ and cosθ have to be positive (i.e. sinθ, cosθ > 0) or sinθ and cosθ both must be negative (i.e. sinθ, cosθ < 0)

The quadrant where sinθ and cosθ are positive is quadrant I. The quadrant where sinθ and cosθ are negative is quadrant III. Hence, tanθ is positive in quadrants I and III only.