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. ยท 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 1735 views around the world You can reuse this answer Creative Commons License