Question

The statement tan theta= -12/5, csc theta=-13/12, and the terminal point determained by theta is in quadrant two

Answer 1

Answer:

cannot be true because csc theta is greater than zero in quadrant 2

Step-by-step explanation:

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Answer 2

Solution:

tan (theta)$=\frac{-12}{5}$$=\frac{\text{Perpendicular}}{\text{Base}}$

Cosec(theta)$=\frac{-13}{12}$$=\frac{\text{Hypotenuse}}{\text{Altitude}}$

In right Triangle,

using Pythagoras theorem

(Hypotenuse)²= (Base)² + (Altitude)²

⇒ (Hypotenuse)²= (12)² + (5)²

⇒Hypotenuse= √(144 +25)

⇒Hypotenuse= 13 cm

As, the value of tan(theta)$=\frac{-12}{5}$ is true if Theta lies in Second Quadrant, but it is not true for Cosec(theta)$=\frac{-13}{12}$  ,if theta lies in second Quadrant, because value of Cosec(theta) is positive in second Quadrant ,irrespective of fact that Terminal side lies in Second Quadrant.

So,  The statement tan (theta)= -12/5, and Cosec (theta)=-13/12, and the terminal point determined by theta is in quadrant two is Incorrect.