SOLUTION: Let f and g be the functions defined by f(x)=sin(x) and g(x)=cos(x). For which of the following values of a is the tangent line to f at x=a parallel to the tangent line to g at x=a

Algebra ->  Trigonometry-basics -> SOLUTION: Let f and g be the functions defined by f(x)=sin(x) and g(x)=cos(x). For which of the following values of a is the tangent line to f at x=a parallel to the tangent line to g at x=a      Log On


   

Question 1050262: Let f and g be the functions defined by f(x)=sin(x) and g(x)=cos(x). For which of the following values of a is the tangent line to f at x=a parallel to the tangent line to g at x=a?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=sin(x) and g(x)=cos(x) ===> f'(x)=cos(x) and g'(x)= -sin(x).
We want f'(a) = g'(a), or cos(a) = -sin(a).
<===> cos(a) + sin(a) = 0.
===>
<===> sqrt%282%29%2Asin%28a%2Bpi%2F4%29+=+0, or sin%28a%2Bpi%2F4%29+=+0
====> a+%2B+pi%2F4+=+k%2Api, where k = ..., -2,-1, 0, 1, 2, 3,.... .
====> highlight%28a+=+-pi%2F4+%2B+k%2Api%29