1.7 Graphs of Polar Equations

What is the general form of a limacon?

• @@r = a + b \times \text{cos}(\theta)@@ or @@r = a + b \times \text{sin}(\theta)@@

• @@r = a - b \times \text{cos}(\theta)@@ or @@r = a - b \times \text{sin}(\theta)@@

• @@r = a + b \times \text{tan}(\theta)@@

• @@r = a^2 + b^2 \times \text{cos}(\theta)@@

What is a polar curve?

• A graph that shows the relationship between distance and angle in polar coordinates.

• A type of graph that only represents linear equations.

• A curve that can only be plotted in Cartesian coordinates.

• A graph that represents the distance from the origin as a function of time.

What type of symmetry does the polar graph @@r = ext{sin}(2 heta)@@ exhibit?

• Symmetry about the x-axis

• Symmetry about the y-axis

• Symmetry about the origin

• Symmetry about the line @@ heta = rac{ ext{ ext{π}}}{4}@@

What is the significance of the pole in polar coordinates?

• The pole is the origin point in polar coordinates, where the distance r is zero.

• The pole represents the maximum distance in polar coordinates.

• The pole is the point where all angles converge in polar coordinates.

• The pole is used to define the direction of the coordinate system.

Define a cardioid in polar coordinates.

• A cardioid is a heart-shaped curve represented by the polar equation @@r = 1 + heta@@ or @@r = 1 - heta@@.

• A cardioid is a circular curve represented by the polar equation @@r = 2 + heta@@.

• A cardioid is a linear curve represented by the polar equation @@r = heta@@.

• A cardioid is a spiral curve represented by the polar equation @@r = heta^2@@.

What does the polar equation @@r = 1 + ext{cos}( heta)@@ represent?

• A circle

• A cardioid

• An ellipse

• A hyperbola

What is a spiral of Archimedes?

• A spiral represented by the polar equation @@r = a + b heta@@, where a and b are constants, and it spirals outward as θ increases.

• A type of spiral that only exists in three-dimensional space.

• A spiral that is defined by a constant radius.

• A spiral that decreases in size as it rotates.

What type of polar curve is represented by the equation @@r = 2 - 3 ext{cos}( heta)@@?

• Inner loop limacon

• Cardioid

• Circle

• Spiral

What is the polar equation for a circle centered at the origin?

• @@r = a@@

• @@r = a^2@@

• @@r^2 = a@@

• @@r = 2a@@

What is the equation of a rose curve?

• @@r = a \times \text{sin}(n\theta)@@

• @@r = a \times \text{tan}(n\theta)@@

• @@r = a \times n\theta@@

• @@r = a \times \text{cos}(2n\theta)@@