Fine the equation of the tangent line to the curve y=sinxcosx at x=π/6 use exact values

Question

Fine the equation of the tangent line to the curve y=sinxcosx at x=π/6 use exact values

Answer 1

The three steps:

Find the derivative of the function (in this case use the product rule)

Find the value of the function and derivative for y_o and y'=m

Put in the values into the point-slope form of the equation for the line.

y = sin x cos x

y'= cos x cos x + sin x(-sin x) = cos² x - sin² x

y(π/6) = sin (π/6) cos (π/6) = (1/2)(√3/2)=√3/4

y'(π/6) = cos² (π/6) - sin² (π/6) = (√3/2)²-(1/2)² = 3/4 -1/4 =1/2

Thus the equation of the line is y - √3/4 = 1/2 (x-(π/6))