Given csc A= 37/12 and that angle A is in Quadrant I, find the exact value of sec A in
simplest radical form using a rational denominator.

Below is the pic of how this would be set up in order to determine what it is you are looking for. The angle is set in QI, and since csc A is the reciprocal of sin, the ratio is hypotenuse over side opposite. Solve for the missing side using Pythagorean's Theorem:

[tex]37^2=12^2+b^2[/tex] and

1369 = 144 + b² and

1225 = b² so

b = 35

The sec ratio is the reciprocal of cos, so if cos is adjacent over hypotenuse, the sec is hypotenuse over adjacent, which is 37/35

Given csc A= 37/12 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator.

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Given csc A= 37/12 and that angle A is in Quadrant I, find the exact value of sec A in
simplest radical form using a rational denominator.