Intervals of Polar equations?

Question

Could anyone help me answer this question: state the smallest interval (0 ≤θ≤ k) that gives the complete graph of the polar equation r = 4cos(5θ). Any help would be grateful. Many thanks. - JJ

Answer 1

The value x gives the same value as θ if 5x = 5θ + 2π

Therefore x = θ + 0.4π

So k = 0.4π

If that seems a bit glib, check:

θ = 0 gives r = 4 cos 0 = 4

θ = 0.4π gives r = 4 cos(5*0.4π)

r = 4 cos(2π) = 4

For θ = 0.4π + x, where 0 ≤ x ≤ 0.4π

r = 4 cos (2π + 5x)

.. = 4 cos(5x)