Question

Given \sec A=\frac{14}{\sqrt{171}}secA= 171 ​ 14 ​ and that angle AA is in Quadrant I, find the exact value of \csc AcscA in simplest radical form using a rational denominator.

Answer 1

Explanation:

`sec A=(14)/(√(171) ) \\cos ~A=(√(171) )/(14) \\sin ~A=√(1-cos^2A) =\sqrt{1-(171)/(196) } =\sqrt{(196-171)/(196) } =\sqrt{(25)/(96) } =\pm(5)/(14) \\csc A=\pm (14)/(5)`

as A is in quadrant 1

`so~csc~A=(14)/(5)`

in quadrant 1 both sin A and csc A are positive.