Given \csc A=\frac{\sqrt{74}}{5}cscA= 5 74 ​ ​ and that angle AA is in Quadrant I, find the exact value of \sec AsecA in simplest radical form using a rational denominator.

Answer 1

If csc A =√74/5 then sin A = 5/√74

You can draw a right triaangle with opposite side 5 units and hypotenuse √74.

By the Pythagorean theorem 74 = 5²+ x²

so x²= 74-5²=74-25=49 and x=±7.

Since the angle is in the first quadrant and cosine is the reciprocal of secant x is positive so

cos A = 7/√74 and sec A =√74/7