Question

Find an equation of he tangent line to the curve at the given point

y= sinx+sin^2 x , (0,0)

Answer 1

y = f(x) = sin x + sin^2 x
f'(x) = cos x + 2sin x cos x
f'(0) = cos 0 + 2sin 0 cos 0 = 1

Let the equation of the tangent be
y = mx + c; where y = 0, m = 1, x = 0
0 = 1(0) + c = 0 + c
c = 0

Therefore, equation of tangent is at point (0, 0) is
y = x