Question

F(t)=sec pi t/4?

Answer 1

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`