Halley's comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by

r = 10.711+0.883sinθ
In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley's comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.

Question

Halley's comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by

r = 10.711+0.883sinθ
In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley's comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.

Narad · Answer

The orbit is
$$r=10.711+0.883 \sin \theta $$
So, you have a function
$$r=f(\theta )$$
When will this function be a maximum?