The curve given by x = sin(t) and y = sin(t + sin(t)) has two tangent lines at the point (x, y) = (0,0). List both of them in order of increasing slope. Your answers should be in the form of y = f(x) without t's. Line with smaller slope: y(x):

Line with larger slope: y(x):

slope of the tangent

The function y = f(x)

 y(x) = 2 x + C

Step-by-step explanation:

Step(i):-

Given x= sin t ...(i)

Differentiating equation (i) with respective to 'x' , we get

Given  y = sin ( t + sin (t)) ...(ii)

Differentiating equation (ii) with respective to 'x' , we get

Step(ii):-

we know that

 x = sin t  

 t = sin⁻¹ (x)

 cost = √1 - sin²(t) = (√1-x²)

Put x =0 and y=0

    d y = 2 d x

Integrating with respective to 'x' , we get

    y(x) = 2 x + C

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

just sum

10 + 10 = 20