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 7030 views around the world You can reuse this answer Creative Commons License