Question Video: Finding the Distance between Two Polar Coordinates Mathematics

Video Transcript

Find the distance between the polar coordinates two, 𝜋 and three, negative three 𝜋 over four. Give your answer accurate to three significant figures.

Remember, to find the distance between two polar coordinates given by 𝑟 one, 𝜃 one and 𝑟 two, 𝜃 two, we use the formula the square root of 𝑟 one squared plus 𝑟 two squared minus two times 𝑟 one 𝑟 two times cos of 𝜃 one minus 𝜃 two. Let’s let 𝑟 one be two and 𝜃 one be 𝜋. So 𝑟 two is three and 𝜃 two is negative three 𝜋 by four. Then, we substitute straight into this formula. And we see the distance between them is the square root of two squared plus three squared minus two times two times three times cos of 𝜋 minus negative three 𝜋 by four. That gives us the square root of 13 minus 12 of cos of seven 𝜋 by four, which is equal to 2.124 and so on. So correct to three significant figures, we see the distance between our polar coordinates is 2.12 units.