Question

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.

Answer 1

To find the exact value of sec A, we use the given csc A and the reciprocal identities for sine and cosine. By substituting the values and simplifying, we can find the exact value of sec A in simplest radical form with a rational denominator.

Step-by-step explanation:

To find the exact value of sec A, we can use the identity sec A = 1/cos A. Since we are given that csc A = 37/12, we can find sin A using the reciprocal identity sin A = 1/csc A. Taking the reciprocal of 37/12, we get sin A = 12/37.

Now we can use the Pythagorean identity sin^2 A + cos^2 A = 1 to find cos A.

Rearranging the equation, we have cos^2 A = 1 - (12/37)^2.

Taking the square root of both sides gives us cos A = sqrt(1 - (12/37)^2).

Finally, we can substitute the values of sin A and cos A into the identity sec A = 1/cos A to find the exact value of sec A in simplest radical form with a rational denominator.