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

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

9

step-by-step explanation: