If 180<A<270 and sinA= -�ã(5)/3, find tan(1/2)A.
To find the value of tan(1/2)A, we need to first determine the value of A. Given that sinA = -�ã(5)/3 and the range of A is 180 degrees < A < 270 degrees, we can use the Pythagorean Identity to find the value of cosA.
The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1.
Since sinA = -�ã(5)/3, we can square it:
(sinA)^2 = (-�ã(5)/3)^2
sin^2(A) = (�ã(5)/3)^2
sin^2(A) = 25/9
Next, we can substitute this value back into the Pythagorean Identity to solve for cosA:
(cosA)^2 = 1 - sin^2(A)
(cosA)^2 = 1 - 25/9
(cosA)^2 = 9/9 - 25/9
(cosA)^2 = -16/9
The value of (cosA)^2 is negative, which means there are no real solutions for cosA in this range. Therefore, we cannot determine the value of A.
As a result, we cannot find the value of tan(1/2)A without knowing the value of A.