What is the slope of the line tangent to the polar curve r 2 cos θ 1 at the point where θ π?

What is the slope of the line tangent to the polar curve r = 2cosΘ – 1 at the point where Θ = π? The slope is undefined.

Why is r cos theta a circle?

r = a cos θ is a circle where “a” is the diameter of the circle that has its left-most edge at the pole. The limaçons containing sine will be above the horizontal axis if the sign between a and b is plus or below the horizontal axis if the sign if minus.

What does r stand for in r Theta?

The formula is S=rθ where s represents the arc length, S=rθ represents the central angle in radians and r is the length of the radius.

How do you find the slope of a tangent line to a polar curve?

To compute slopes of tangent lines to a polar curve r=f(θ), we treat it as a parametrized curve with θ=t and r=f(t). (Equivalently, we can use θ as our parameter). This means that x=rcos(θ)=f(t)cos(t);y=rsin(θ)=f(t)sin(t). Taking derivatives we get dx/dt=−f(t)sin(t)+f′(t)cos(t);dy/dt=f(t)cos(t)+f′(t)sin(t).

How do you plot a polar curve on a graph?

To plot a polar curve, find points at increments of theta, then plot them on polar axes. Graph the polar curves on the same axes. Using the table of standard curves, we can plot all of these on the same axes. r = 4 r=4 r = 4 is like r = a r=a r = a, so it’s a circle centered at ( 0, 0) (0,0) ( 0, 0) with radius 4 4 4.

How do you find the standard form of a polar curve?

If we can’t use the table above to find a standard form for the polar curve we’re given, then we can always generate a table of coordinate points ( r, θ) (r, heta) ( r, θ). In order to do that, we’ll take the value inside the trigonometric function that includes θ heta θ, set it equal to π / 2 \\pi/2 π / 2, then solve for θ heta θ.

How to find the value of θ Heta θ?

In order to do that, we’ll take the value inside the trigonometric function that includes θ heta θ, set it equal to π / 2 \\pi/2 π / 2, then solve for θ heta θ. For example, given the polar curve r = 6 sin 3 θ r=6\\sin {3 heta} r = 6 sin 3 θ,