Question

Find the coordinates of the point (x,y) at the given angle θ on a circle of radius r centered at the origin. Show all work. Round decimal to three places. (5 points) θ=215° and r=4 Type equation here. Type equation here. (5 points) θ=-30° and r=1 Type equation here. Type equation here.

Answer 1

(i) The equivalent coordinates in rectangular form are
`(x, y) = (-3.277,-2.294)`.

(ii) The equivalent coordinates in rectangular form are
`(x, y) = (0.866, 0.5)`.

Explanation:

In this exercise we must find the equivalent coordinates in rectangular form from polar form. That is:

`(x, y) = (r\cdot \cos \theta, r\cdot \sin \theta)`

Where:

`r` - Norm of vector, dimensionless.

`\theta` - Direction of vector with respect to +x semiaxis, measured in sexagesimal degrees.

(i) (
`r = 4`,
`\theta = 215^(\circ)`)

`(x. y) = (4\cdot \cos 215^(\circ), 4\cdot \sin 215^(\circ))`

`(x, y) = (-3.277,-2.294)`

The equivalent coordinates in rectangular form are
`(x, y) = (-3.277,-2.294)`.

(ii) (
`r = 1`,
`\theta = 30^(\circ)`)

`(x. y) = (1\cdot \cos 30^(\circ), 1\cdot \sin 30^(\circ))`

`(x, y) = (0.866, 0.5)`

The equivalent coordinates in rectangular form are
`(x, y) = (0.866, 0.5)`.