Question

If cos A = 3 over 11, then which of the following is correct?

Answer 1

Answer:  The answer is (a) sec A = 11 over 3.

Step-by-step explanation: Given that Cosine of an angle 'A' is 3 over 11,

i.e.,

$\cos A=\dfrac{3}{11}.$

And we need to find which one of the given four options is correct.

We have the following relations between cosine, secant and cosecant of an angle from trigonometry.

$\sec A=\dfrac{1}{\cos A}~~\textup{and}~~\csc A=\dfrac{1}{\sqrt{1-\cos^2 A}}.$

Therefore,

$\sec A=\dfrac{11}{3}$

and

$\csc A=\dfrac{1}{\sqrt{1-\frac{9}{121}}}=\dfrac{1}{\sqrt{\frac{112}{121}}}=\dfrac{11}{4\sqrt 7}.$

Thus, the correct option is (a)  sec A = 11 over 3.