What is the equation of the line tangent to #f(x)=cos x + sin^2 x # at #x=0#? Calculus Derivatives Tangent Line to a Curve 1 Answer Jim G. · mason m Jan 5, 2016 #y = 1# Explanation: #f(x) = cos x + sin^2x # #f'(x) = - sinx + 2sinx ( cosx) = 2sinxcosx - sinx# at #x = 0#: #f'(0) = 2sin0 cos0 - sin0 = 0# now since the slope of the tangent line #= 0# the tangent will be parallel to the #x#-axis with the equation #y = k# where #k# is a constant. #f(0) = cos 0 +(sin0)^2 = 1# # rArr y=1 # is the equation of the line tangent. 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 1396 views around the world You can reuse this answer Creative Commons License