re: 1//2 Penalty: 1 off Watch Video Show Examples fiven cot A=-(5)/(sqrt171) and that angle A is in Quadrant IV, find the exact value of sin A n simplest radical form using a rational denominator. Answer Attempt 2 out of 3 -sqrt171 Submit Answer

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re:  1//2 Penalty: 1 off Watch Video Show Examples fiven  cot A=-(5)/(sqrt171) and that angle  A is in Quadrant IV, find the exact value of  sin A n simplest radical form using a rational denominator. Answer Attempt 2 out of 3  -sqrt171 Submit Answer

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Use Pythagorean Identity: Use the Pythagorean identity for cotangent and sine: cot^2(A) + 1 = csc^2(A). Since we know cot A, we can find csc A and then sin A.Calculate csc^2(A): Calculate csc^2(A) using the identity: csc^2(A) = cot^2(A) + 1. Substitute cot A = -(5)/(sqrt(171)) into the identity. csc^2(A) = [-(5)/(sqrt(171))]^2 + 1 csc^2(A) = (25/171) + 1 csc^2(A) = (25/171) + (171/171) csc^2(A) = (196/171)Find csc(A): Find csc(A) by taking the square root of csc^2(A). csc(A) = sqrt(196/171) csc(A) = sqrt(196)/sqrt(171) csc(A) = 14/sqrt(171) Since we need a rational denominator, rationalize the denominator. csc(A) = (14/sqrt(171)) * (sqrt(171)/sqrt(171)) csc(A) = (14*sqrt(171))/171Find sin(A): Since csc(A) is the reciprocal of sin(A), we can find sin(A) by taking the reciprocal of csc(A). sin(A) = 1/csc(A) sin(A) = 1/((14*sqrt(171))/171) sin(A) = 171/(14*sqrt(171))Simplify sin(A): Simplify the expression for sin(A) by dividing both the numerator and the denominator by the greatest common divisor, which is 14. sin(A) = (171/14)/(sqrt(171)*14/14) sin(A) = (171/14)/(sqrt(171)) sin(A) = (171/14) * (1/sqrt(171)) sin(A) = 171/(14*sqrt(171))Include negative sign: Since angle A is in Quadrant IV, sin A must be negative. Therefore, we must include the negative sign in our final answer. sin(A) = -171/(14*sqrt(171))

$\newline$ Given $\cot A=-\frac{5}{\sqrt{171}}$ and that angle $A$ is in Quadrant IV, find the exact value of $\sin A$ n simplest radical form using a rational denominator. $\newline$ Answer____

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\newlineGiven cot⁡A=−5171 \cot A=-\frac{5}{\sqrt{171}} cotA=−171​5​ and that angle A A A is in Quadrant IV, find the exact value of sin⁡A \sin A sinA n simplest radical form using a rational denominator.\newlineAnswer____

$\newline$ Given $\cot A=-\frac{5}{\sqrt{171}}$ and that angle $A$ is in Quadrant IV, find the exact value of $\sin A$ n simplest radical form using a rational denominator. $\newline$ Answer____