Let p be a point at a distance d from the center of a circle of radius r. the curve traced out by p as the circle rolls along a straight line is called a trochoid. (think of the motion of a point on a spoke of a bicycle wheel.) the cycloid is the special case of a trochoid with d = r. using the same parameter θ as for the cycloid and, assuming the line is the x-axis and θ = 0 when p is at one of its lowest points, show that parametric equations of the trochoid are x=rθ-d sin θ , y = r - d cos θ. sketch the trochoid for the cases d < r and d > r.

b

step-by-step explanation:

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c