Answer:
(i) The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
Step-by-step explanation:
In this exercise we must find the equivalent coordinates in rectangular form from polar form. That is:
[tex](x, y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where:
[tex]r[/tex] - Norm of vector, dimensionless.
[tex]\theta[/tex] - Direction of vector with respect to +x semiaxis, measured in sexagesimal degrees.
(i) ([tex]r = 4[/tex], [tex]\theta = 215^{\circ}[/tex])
[tex](x. y) = (4\cdot \cos 215^{\circ}, 4\cdot \sin 215^{\circ})[/tex]
[tex](x, y) = (-3.277,-2.294)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) ([tex]r = 1[/tex], [tex]\theta = 30^{\circ}[/tex])
[tex](x. y) = (1\cdot \cos 30^{\circ}, 1\cdot \sin 30^{\circ})[/tex]
[tex](x, y) = (0.866, 0.5)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
