# Thread: finding the equation of a tangent

1. ## finding the equation of a tangent

i for the x and y value but i need help finding the slope.

the equation is f(x) = tanx at x=pi/4

i know the derivative of this is sec^2(x)

so y = sec^2(pi/4)

i dont know how to get the value of this

2. Originally Posted by proski117
i for the x and y value but i need help finding the slope.

the equation is f(x) = tanx at x=pi/4

i know the derivative of this is sec^2(x)

so y = sec^2(pi/4)

i dont know how to get the value of this
$\frac{\pi}{4}$ is on the standard triangle. $sec^2(x) = \frac{1}{cos^2(x)}$

As $cos{\frac{\pi}{4}} = \frac{\sqrt(2)}{2}$ so

$cos^2{\frac{\pi}{4}} = \frac{1}{2}$

therefore $cos^2{\frac{\pi}{4}} = 2$