Have you ever wondered what the circumference of the Earth is? Well, at the Equator, the distance around is about 25000 miles (assuming the Earth is sphere). What if you wanted to know the distance around at any latitudinal location? For instance, if you traveled along the Arctic Circle all the way around, how many miles would you actually go? This problem is all about latitudinal travel at various degrees of latitude:
Let C be the distance around Earth at latitude location alpha. Find a formula that will calculate C for any value of alpha. Then use this formula to find the following distances (it should also work at the Equator, yes..show this)
Around the Earth at the Tropic of Cancer/Capricorn (23.5 latitude)
Around the Earth at the Arctic/ Antarctic Circle (66.5 latitude)
Around the Earth at the North/ South Pole (90 latitude)
Around the Earth at Portland's latitude (45.5 latitude)

$\theta$ = latitude

$r(\theta)$ = radius as a function of latitude

$R$ = Earth Radius