Given tan A=-(11)/(60) and that angle A is in Quadrant IV, find the exact value of csc A in simplest radical form using a rational denominator.

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Given Information: We are given that tan A = -(11/60) and that angle A is in Quadrant IV. In the fourth quadrant, the tangent function is negative because sine is negative and cosine is positive. We can use the Pythagorean identity for tangent, which is tan² A + 1 = sec² A, to find sec A and then use that to find csc A.Find sec A: First, let's find sec A using the identity tan² A + 1 = sec² A. We substitute tan A with -(11/60) to find sec² A. sec² A = tan² A + 1 sec² A = (-11/60)² + 1 sec² A = (121/3600) + 1 sec² A = (121/3600) + (3600/3600) sec² A = (121 + 3600) / 3600 sec² A = 3721 / 3600Find csc A: Now, we take the square root of sec² A to find sec A. Since A is in the fourth quadrant, sec A will be positive. sec A = √(3721/3600) sec A = √3721 / √3600 sec A = 61/60Find cos A: The cosecant function is the reciprocal of the sine function, so csc A = 1/sin A. Since sec A is the reciprocal of cos A, and we have the Pythagorean identity sin² A + cos² A = 1, we can find sin A using the relationship sin² A = 1 - cos² A.Find sin A: We know that cos A = 1/sec A, so we can find cos A first. cos A = 1/sec A cos A = 1/(61/60) cos A = 60/61Find csc A: Now we use the identity sin² A + cos² A = 1 to find sin² A. sin² A = 1 - cos² A sin² A = 1 - (60/61)² sin² A = 1 - (3600/3721) sin² A = (3721/3721) - (3600/3721) sin² A = (3721 - 3600) / 3721 sin² A = 121 / 3721We take the square root of sin² A to find sin A. Since A is in the fourth quadrant, sin A will be negative. sin A = -√(121/3721) sin A = -√121 / √3721 sin A = -11/61Finally, we find csc A, which is the reciprocal of sin A. csc A = 1/sin A csc A = 1/(-11/61) csc A = -61/11

Given $\tan A=-\frac{11}{60}$ and that angle $A$ is in Quadrant IV, find the exact value of $\csc A$ in simplest radical form using a rational denominator.

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Given tan⁡A=−1160 \tan A=-\frac{11}{60} tanA=−6011​ and that angle A A A is in Quadrant IV, find the exact value of csc⁡A \csc A cscA in simplest radical form using a rational denominator.

Given $\tan A=-\frac{11}{60}$ and that angle $A$ is in Quadrant IV, find the exact value of $\csc A$ in simplest radical form using a rational denominator.