Final answer:
To find sin(x) given that cot(x) = 13/23 in quadrant I, we can use trigonometric identities to find the value of sin(x).
Step-by-step explanation:
To find sin(x) given that cot(x) = 13/23 in quadrant I, we can use the following trigonometric identity:
sin^2(x) + cos^2(x) = 1
Since cot(x) = 13/23, we can find the value of cos(x) using the identity:
cos(x) = 1/sqrt(1+(cot(x))^2) = 1/sqrt(1+(13/23)^2) = 1/sqrt(1+169/529) = 1/sqrt(698/529) = sqrt(529/698) = 23/sqrt(698)
Then, we can solve for sin(x) using the fact that cos^2(x) + sin^2(x) = 1:
sin^2(x) = 1 - cos^2(x) = 1 - (23/√698)^2 = 1 - 529/698 = 169/698
sin(x) = ±√(169/698)
Since x is in quadrant I, sin(x) is positive. Therefore, sin(x) = √(169/698) = 13/√698