Question

What trigonometric ratios give negative values in III quadrant?

• A. A.tan & cot
• B. B.sin & cosec
• C. C.cos & sec
• D. Both B & C
• E. Both A& B

Answer 1

The correct option is D

Both B & C

In third quadrant, only tan$\theta$ & cot$\theta$ positive values because, trigonometric ratio of tan$\theta$ & cot$\theta$

includes ratio of adjacent & opposite and in lll quadrant both adjacent & opposite are negative.

Positive Trignometric Function

$\begin{array}{cc}\text{II sin}\theta \text{and cosec}\theta & \text{I Alltrigonometric function}\\ \text{III tan}\theta \text{and cot}\theta & \text{IV sec}\theta \text{and cosec}\theta \end{array}$

So, only tan$\theta$ & cot$\theta$ give positive value in III quadrant.All the trigonometric function except

tan$\theta$ & cot$\theta$ give negative values in III quadrant