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
Use product rule:
$\displaystyle f'(x)=\cos(x) \cdot \cos(x) + \sin(x) \cdot (-\sin(x)) = \cos^2(x)-\sin^2(x) =$ $\displaystyle \cos^2(x) -(1-\cos^2(x) = 2\cos^2(x) - 1$
Then $\displaystyle f'(\frac{\pi}{4}) = 0$ and therefore the equation of the tangent is $\displaystyle y = \frac12$