Question

Given csc(A) = 65/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!

Answer 1

Answer:

$secA = \frac{65}{63}$

Step-by-step explanation:

$cosec A = \frac{65}{16}\\\\sin A = \frac{1}{cosecA} = \frac{16}{65}\\\\cos^2 A = 1 - sin^2 A$

        $= 1 - (\frac{16}{65})^2\\\\=\frac{4225-256}{4225}\\\\=\frac{3969}{4225}$

$cos A = \sqrt{\frac{3696}{4225}} = \frac{63}{65}$

$secA = \frac{1}{cosA} = \frac{65}{63}$