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

`secA = (65)/(63)`

Explanation:

`cosec A = (65)/(16)\\\\sin A = (1)/(cosecA) = (16)/(65)\\\\cos^2 A = 1 - sin^2 A`

`= 1 - ((16)/(65))^2\\\\=(4225-256)/(4225)\\\\=(3969)/(4225)\\`

`cos A = \sqrt{(3696)/(4225)} = (63)/(65)`

`secA = (1)/(cosA) = (65)/(63)`