Question

If cot(x) = 13/23 (in quadrant I). what is sin(x)?
A. f(−3)=−1 and f(10)=15

Answer 1

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