finding slope of tangent line

Question

anonymous · Answer

Find the slope of the tangent line at f(x) = 2cosx at x = pi/3

anonymous · Answer

@Callisto

callisto · Answer

Find f'(x), then, find f'(pi/3)
Do you know how to find f'(x)?

anonymous · Answer

yeah, however I got this from a a previous semester exam. And the lecturer used a formula that goes like this, which I am totally confused about:

m = (f(x)cosx+f'(x)sinx / -f(x)sinx+f'(x)cosx)

His answer was $$\frac{ 1 }{ \sqrt{3} }$$

anonymous · Answer

I got an answer of $$-\sqrt{3}$$

@Callisto

anonymous · Answer

@callisto http://apps.dso.iastate.edu/si/documentdb/fall_2010/MATH_166__GHJK__Hentzel_jasmine1_Math_166_Final_Review_Sol_n..pdf Scroll down to Page 12.

callisto · Answer

Because it's in polar coordinates, while the method I mentioned was in rectangular coordinates, so that method doesn't work for your question!

anonymous · Answer

how would you know if its in polar coordinates?

callisto · Answer

If the equation is r = something in theta, for 99.9%, it would be in polar coordinates

anonymous · Answer

ahhh. Im still doing semester 1 and was looking at past papers hahaha. Went to the wrong question! thanks tho!

callisto · Answer

Welcome :)