How do you find the equation of the tangent line to the curve #y=sinx+sin^2x# at (0,0)?

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Answer 1 · 2017-08-16T02:25:27

Compute the first derivative:

#dy/dx = cos(x)+sin(2x)#

The slope, m, of the tangent line is the above evaluated at #x = 0#:

#m = cos(0)+sin(2(0))#

#m = 1#

Use the point-slope form of the equation of a line:

#y = m(x-x_1)+y_1#

The slope, #m = 1# and the point #(0,0)# tells us that #x_1 = 0, and y_1 = 0#:

#y = 1(x-0)+0#

#y = x larr# this is the equation of the tangent line