Given sec A=(sqrt61)/(6) and that angle A is in Quadrant I, find the exact value of csc A in simplest radical form using a rational denominator.

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Given  sec A=(sqrt61)/(6) and that angle  A is in Quadrant I, find the exact value of  csc A in simplest radical form using a rational denominator.

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Understand relationship sec A cos A: Understand the relationship between sec A and cos A. Secant is the reciprocal of cosine. sec A = 1 / cos A Given sec A = (sqrt(61))/6, we can find cos A by taking the reciprocal of sec A.Calculate cos A: Calculate cos A. cos A = 1 / sec A cos A = 1 / ((sqrt(61))/6) cos A = 6 / sqrt(61) To rationalize the denominator, multiply the numerator and denominator by sqrt(61). cos A = (6 / sqrt(61)) * (sqrt(61) / sqrt(61)) cos A = (6 * sqrt(61)) / 61Use Pythagorean identity find sin A: Use the Pythagorean identity to find sin A. The Pythagorean identity states that sin^2 A + cos^2 A = 1. We know cos A, so we can solve for sin^2 A. sin^2 A = 1 - cos^2 A sin^2 A = 1 - ((6 * sqrt(61)) / 61)^2 sin^2 A = 1 - (36 * 61) / (61 * 61) sin^2 A = 1 - (36 * 61) / 3721 sin^2 A = (3721 - 2196) / 3721 sin^2 A = 1525 / 3721 Since A is in Quadrant I, sin A is positive. sin A = sqrt(1525) / sqrt(3721) sin A = sqrt(1525) / 61Find csc A: Find csc A, which is the reciprocal of sin A. csc A = 1 / sin A csc A = 1 / (sqrt(1525) / 61) To rationalize the denominator, multiply the numerator and denominator by sqrt(1525). csc A = (61 / sqrt(1525)) * (sqrt(1525) / sqrt(1525)) csc A = (61 * sqrt(1525)) / 1525Simplify expression csc A: Simplify the expression for csc A. We need to simplify sqrt(1525). Since 1525 = 25 * 61, we can take the square root of 25 out of the radical. csc A = (61 * sqrt(25 * 61)) / 1525 csc A = (61 * 5 * sqrt(61)) / 1525 csc A = (305 * sqrt(61)) / 1525 Now, simplify the fraction by dividing both the numerator and the denominator by 305. csc A = sqrt(61) / 5

Given $\sec A = \frac{\sqrt{61}}{6}$ and that angle $A$ is in Quadrant I, find the exact value of $\csc A$ in simplest radical form using a rational denominator.

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Given sec⁡A=616 \sec A = \frac{\sqrt{61}}{6} secA=661​​ and that angle A A A is in Quadrant I, find the exact value of csc⁡A \csc A cscA in simplest radical form using a rational denominator.

Given $\sec A = \frac{\sqrt{61}}{6}$ and that angle $A$ is in Quadrant I, find the exact value of $\csc A$ in simplest radical form using a rational denominator.