What is the local linearization of #F(x) = cos(x) # at a=pi/4? Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer Bdub Apr 4, 2016 #L(x)=sqrt2/2-sqrt2/2 (x-pi/4)# Explanation: #L(x)=f(a)+f'(a)(x-a)# #F(a)=cos (pi/4)=sqrt2/2# #F'(a)=-sin(pi/4)=-sqrt2/2# #L(x)=sqrt2/2-sqrt2/2 (x-pi/4)# Answer link Related questions How do you find the linear approximation of #(1.999)^4# ? How do you find the linear approximation of a function? How do you find the linear approximation of #f(x)=ln(x)# at #x=1# ? How do you find the tangent line approximation for #f(x)=sqrt(1+x)# near #x=0# ? How do you find the tangent line approximation to #f(x)=1/x# near #x=1# ? How do you find the tangent line approximation to #f(x)=cos(x)# at #x=pi/4# ? How do you find the tangent line approximation to #f(x)=e^x# near #x=0# ? How do you use the tangent line approximation to approximate the value of #ln(1003)# ? How do you use the tangent line approximation to approximate the value of #ln(1.006)# ? How do you use the tangent line approximation to approximate the value of #ln(1004)# ? See all questions in Using the Tangent Line to Approximate Function Values Impact of this question 6835 views around the world You can reuse this answer Creative Commons License