# Thread: Finding the tangent line!

1. ## Finding the tangent line!

Find the equation of the line tangent to the curve y = (sin(x))(cos(x))
at the point (pi/4, 1/2).

im usually good with finding tangent lines from this kinda stuff, but this one doesnt seem to work for me...any help

thanks

2. Originally Posted by mathlete
Find the equation of the line tangent to the curve y = (sin(x))(cos(x))
at the point (pi/4, 1/2).

...
Use product rule:

$f'(x)=\cos(x) \cdot \cos(x) + \sin(x) \cdot (-\sin(x)) = \cos^2(x)-\sin^2(x) =$ $\cos^2(x) -(1-\cos^2(x) = 2\cos^2(x) - 1$

Then $f'(\frac{\pi}{4}) = 0$ and therefore the equation of the tangent is $y = \frac12$