10. Consider the polar equation r = sin² (2) a) Find the (rectangular) equation of the tangent line when 0 => b) Set up an integral to represent the arc length of the curve for 0

Graph the curve with parametric equations  x = sin(t), y = 3 sin(2t), z = sin(3t). Find the total length of this curve correct to four decimal places.

Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

The curve r = VI + sin20,

Trace the curve: r = 2+3 cos 0.

B) Find the length of the curve r = 1+ sin(26) V20

Trace the curve r² = 4cos⁴(theta) tan²(theta).

Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4

The path of a projectile is modeled by the parametric equations                        x = (90 cos 30°)t and y = (90 sin 30°)t − 16t2                                                    where x and y are measured in feet. (a) Use a graphing utility to graph the path of the projectile. (b) Use a graphing utility to approximate the range of the projectile. (c) Use the integration capabilities of a graphing utility to approximate the arc length of the path. Compare this result with the range of the projectile

A bumblebee is flying so that its position is given by~r(t) = cos(2t), cos(3t),sin(5t) for the osculating circle at t = π/6, find either the equation, or a set of parametricequations describing this osculating circle.