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.

Explanation:

Apex trigonometry answer

Answer 2

Answer with explanation:

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

`\cot A =(12* \sec A)/(5)\\\\ (\cos A)/(\sin A)=(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=(-12 \pm √(12^2-4* -5 * 5))/(2 * 5)\\\\\sin A=(-12 \pm √(144+100))/(10)\\\\ \sin A=(-12 \pm √(244))/(10)\\\\ \sinA=(-12\pm 15.6)/(10)\\\\ \sin A=(-12 +15.6)/(10)\\\\ as, -1\leq SinA \leq +1\\\\ \sin A=(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 =(12)/(5)`

And , A lies in second Quadrant,

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