Question

Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle

using radians in terms of te over the interval 0

Answer 1

`(6√(3),\,(5\pi)/(6))`

Explanation:

The radius r can be found from the relationship

`r^2=x^2+y^2\\r^2=(-9)^2+(3√(3))^2\\r^2=81+27=108\\r=√(108)\\r=6√(3)`

The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.

`cos(\theta)=(x)/(r)=(-9)/(6√(3))\\cos(\theta)=-(9)/(6√(3)) \cdot (√(3))/(√(3))\\cos(\theta)=-(9√(3))/(6\cdot3)\\cos(\theta)=-(√(3))/(2)\\\\\cos^(-1)(-√(3))/(2)}=(5\pi)/(6)`

See the attached image.