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 = sin x + sin² x
y ` = f ` ( x ) = cos x + 2 sin x cos x
f `( 0 ) = cos 0 + 2 sin 0 cos 0 = 1
The tangent line formula:
y - y0 = f ` ( x0 ) ( x - x0 )
y - 0 = 1 · ( x - 0 )
Answer: y = x