Question

The statement “cot theta= 12/5, sec theta, and the terminal point determined by theta is in quadrant 2.”

Answer 1

Answer: cannot be true because cot∅ is less than zero in quadrant 2.

Step-by-step explanation:

Apex trigonometry answer

Answer 2

Answer with explanation:

If theta is replaced by , A,then the given statement will become

$\cot A =\frac{12\times \sec A}{5}\\\\ \frac{\cos A}{\sin A}=\frac{12}{5\cos A}\\\\5 \cos^2 A=12 \sin A\\\\5(1-\sin^2 A)=12 \sin A\\\\5-5\sin^2 A=12 \sin A\\\\ 5 \sin^2 A+12 \sin A -5=0\\\\ \sin A=\frac{-12 \pm \sqrt{12^2-4\times -5 \times 5}}{2 \times 5}\\\\\sin A=\frac{-12 \pm \sqrt{144+100}}{10}\\\\ \sin A=\frac{-12 \pm \sqrt{244}}{10}\\\\ \sinA=\frac{-12\pm 15.6}{10}\\\\ \sin A=\frac{-12 +15.6}{10}\\\\ as, -1\leq SinA \leq +1\\\\ \sin A=\frac{3.6}{10}\\\\ \sin A=0.36$  

Which will be positive in second Quadrant.So,it is a true statement.

→If the statement is ,      

$\cot A =\frac{12}{5}$

And , A lies in second Quadrant,

Only ,Sine and Cosecant, Function are Positive in Second Quadrant.So,the statement, will be incorrect.