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

Answer:

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

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

Step-by-step 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 $(x, y) = (0.866, 0.5)$.