your derivative is correct.
now just plug in x = π/2 to get the slope
remember that tan(π/2) is undefined, BUT
cot (π/2) = cos(π/2) / sin(π/2) = 0/1 = 0
so slope = -csc^2 (π/2) = 2
I calculated and got -1 as the slope. Can you please explain how you got 2 for the slope?
To find the slope of a function at a specific point, we need to plug in the x-coordinate of the point into the derivative function. In this case, we have already calculated the derivative and obtained -csc^2(x).
To find the slope at x = π/2, we need to substitute this value into the derivative function:
slope = -csc^2(π/2).
Now, let's evaluate this expression. Keep in mind that the csc function is the reciprocal of the sine function: csc(x) = 1/sin(x).
When we substitute x = π/2, we have:
slope = -csc^2(π/2) = -(1/sin(π/2))^2.
Next, we need to simplify further. The sine of π/2 is 1, so the expression becomes:
slope = -(1/1)^2 = -1^2 = -1 * -1 = 1.
Therefore, the correct slope at x = π/2 is 1, not 2.