Question

In: Math

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve...

Solve the problem

43) Find equations for the horizontal and vertical tangent lines to the curve r = 1 - sinθ, 0 ≤ θ < 2π.

Please check if your answer is correct with the following:

Horizontal: y = 1/4 at (1/2, π/6), y = 1/4 at (1/2, 5π/6), y = -2 at (2, 3π/2)

Vertical: x = 0 at (0, π/2), x = -3sqrt(3)/4 at (3/2, 7π/6), x = 3sqrt(3)/4 at (3/2, 11π/6)

Solutions

Expert Solution


Related Solutions

For the curve r=1+sin(theta), find: Location of horizontal tangent lines: Location of vertical tangent lines:
For the curve r=1+sin(theta), find: Location of horizontal tangent lines: Location of vertical tangent lines:
Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3...
Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3 - 3t +1, y(t) = 4t^2 +5. then write our the equations for the tangent lines
Find parametric equations for the tangent line to the curve with the given parametric equations at...
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
Find equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that...
Find equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that pass through the point (27, 3)
Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = x2 + y2,    z = 16 − y,    (4, −1, 17)
Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)
Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.
Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$
Find the equations for the tangent line and the normal line to the curve x^2 +...
Find the equations for the tangent line and the normal line to the curve x^2 + arcsin(x + y − 1) = y^2sqrt(8x) at the point (2, −1)..
Find the equations of the tangent lines to the circle x^2 + y^2 = 9 which...
Find the equations of the tangent lines to the circle x^2 + y^2 = 9 which pass through the point (−7, 2). (Ans.: Using decimal approximations, the lines are approximately y = −0.847493x − 3.932456 and 0.147493x + 3.032456.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT