F(t)=sec pi t/4?

1 Answer
Apr 10, 2018

I'm assuming your asking for the derivative or integral since your question is tagged calculus.

Explanation:

Derivative:
F(t) = sec((pit)/4)

F(t) = (cos((pit)/4))^-1

F'(t) = -(cos((pit)/4))^-2 xx -sin((pit)/4) xx pi/4

F'(t) = (pisin((pit)/4))/(4cos^2((pit)/4))

F'(t) = pi/4tan((pit)/4)sec((pit)/4)

Integral:

I =int sec((pit)/4) dt

I = int sec((pit)/4) xx(sec((pit)/4) + tan((pit)/4))/(sec((pit)/4)+ tan((pit)/4)) dt

I = 4/(pi)int (pi/4sec^2((pit)/4) + pi/4sec((pit)/4)tan((pit)/4))/(sec((pit)/4)+ tan((pit)/4)) dt

I = 4/piln(sec((pit)/4) + tan((pit)/4)) + C