3.14 Polar Function Graphs

Front

What is a polar function?

Back

A polar function is a function that defines a relationship between the radius (r) and the angle (θ) in polar coordinates, typically expressed as r = f(θ).

Front

What is the range of θ for the polar function r = θ?

Back

The range of θ for the polar function r = θ is 0 ≤ θ ≤ 3π/2.

Front

What does the graph of r = θ look like in polar coordinates?

Back

The graph of r = θ is a spiral that starts at the origin and moves outward as θ increases.

Front

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

Back

The polar function for a circle centered at the origin is r = a, where 'a' is the radius of the circle.

Front

What is the polar function for a cardioid?

Back

The polar function for a cardioid is r = a(1 + cos(θ)) or r = a(1 + sin(θ)), where 'a' is a constant.

Front

What is the significance of the coefficient in r = a cos(θ)?

Back

The coefficient 'a' determines the size of the graph and its distance from the origin.

Front

What is the polar function for a rose curve?

Back

The polar function for a rose curve is r = a sin(nθ) or r = a cos(nθ), where 'n' determines the number of petals.

Front

How does the graph of r = 6 cos²(θ) behave?

Back

The graph of r = 6 cos²(θ) produces a circle that varies in size based on the angle θ.

Front

What is the period of the function r = 6sin(4θ)?

Back

The period of the function r = 6sin(4θ) is π/2, meaning it completes one full cycle in that interval.

Front

What is the effect of changing the value of 'n' in r = a sin(nθ)?

Back

Changing 'n' affects the number of petals in the rose curve; if 'n' is even, the number of petals is 2n, and if odd, it is n.