Final answer:
To find tan(x)/(2), we need to find the value of tan(x) and divide it by 2. Given that cos(x) = -4/5 and x is in the second quadrant, we can use the equation sin^2(x) + cos^2(x) = 1 to find sin(x). Finally, we divide the value of tan(x) by 2 to get the result.
Step-by-step explanation:
To find tan(x)/(2), we need to find the value of tan(x) and divide it by 2. Given that cos(x) = -4/5 and x is in the second quadrant, we can use the equation sin^2(x) + cos^2(x) = 1 to find sin(x). Since sin(x) is positive in the second quadrant, we have sin(x) = sqrt(1 - cos^2(x)) = sqrt(1 - (-4/5)^2) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5.
Now, we can find tan(x) = sin(x)/cos(x) = (3/5)/(-4/5) = -3/4. Finally, we divide -3/4 by 2 to get the result: tan(x)/(2) = (-3/4)/(2) = -3/8.