How do you sketch the graph of the polar equation and find the tangents at the pole of #r=2(1sintheta)#?
Tracing the cardioid from pole to pole, in the positive anticlockwise sense, we start in the direction
graph{x^2+y^2+2y2sqrt(x^2+y^2)=0 [10, 10, 5, 5]}
I think that it is my duty to answer in the way that is right to me.
In polar curves through the pole, some do have a node at the pole.
This node has two tangents ( including the pair, in the opposite
directions ).
In (2D or 3D) polar coordinates, the pole is a point that has to be
assigned an ad hoc direction. for the chosen application. Here it is
graphing..
Tracing any curve is done by moving the marker in the direction of
the tangent.
In polar form, this is
using L'Hospital rule.
the slope is 1. We can say that these directions are given by #theta =
Tracing the cardioid from pole to pole, in the positive anticlockwise
Verification : Practical.
By signing up, you agree to our Terms of Service and Privacy Policy
To sketch the graph of the polar equation ( r = 2(1  \sin(\theta)) ) and find the tangents at the pole, follow these steps:

Plot Key Points:
 Substitute different values of ( \theta ) to find corresponding values of ( r ).
 Plot these points on a polar coordinate system.

Determine Symmetry:
 Check for symmetry about the polar axis (( \theta = 0 )) and the line ( \theta = \frac{\pi}{2} ) to simplify the graphing process.

Sketch the Graph:
 Connect the plotted points smoothly to form the curve.

Find Tangents at the Pole:
 To find tangents at the pole, first, express ( r ) in terms of ( \theta ) and differentiate with respect to ( \theta ).
 Substitute ( \theta = 0 ) into the derivative to find the slope of the tangent at the pole.
 Use this slope and the point (0,0) to write the equation of the tangent line in polar form.

Optional: Plot Tangent Lines:
 Plot the tangent lines on the polar coordinate system using the polar equation obtained in the previous step.

Label Key Features:
 Label the pole and any other relevant points or features on the graph.

Finalize:
 Review the graph to ensure accuracy and clarity.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 What is the distance between the following polar coordinates?: # (4,(5pi)/3), (3,(7pi)/6) #
 What is the slope of the polar curve #f(theta) = sectheta  csctheta # at #theta = (5pi)/4#?
 How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3sin2theta#?
 What is the distance between the following polar coordinates?: # (3,(pi)/2), (2,(13pi)/12) #
 What is the polar form of #( 11,14 )#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7