What is the equation of the tangent line of # f(x)=sinpix-cospix # at # x=3 #? Calculus Derivatives Tangent Line to a Curve 1 Answer Bdub Apr 14, 2016 #f(x)=1-pi(x-3)# Explanation: #f'(x)=picospix+pisinpix# Slope at x=3: #f'(3)=picos3pi+pisin3pi=-pi+0=-pi# Point: #f(3)=sin3pi-cos3pi=0-(-1)=1;(3,1)# Equation: #f(x)=f(a)+f'(a)(x-a)# #f(x)=1-pi(x-3)# Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve #3y^2-2x^2=1#? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 1461 views around the world You can reuse this answer Creative Commons License