Question

2. Convierte los siguientes ángulos de coordenadas polares a coordenadas
cartesianas (no olvides dibujarlos en los ejes correspondientes).
A= (5,45°)
B= (2, 160°)
C= (4, 200°)
D= (1, 300°)
E= (3, 1.4PI)

Answer 1

La conversión de las coordenadas polares a coordenadas cartesianas es:

A = (5,45°) = A(5√2/2; 5√2/2)

B = (2, 160°) = B(-1.88; 0.68)

C= (4, 200°) = C(-3.76; -1.37)

D= (1, 300°) = D(1/2; -√3/2)

E= (3, 1.4π) = E(-0.92; -2.85)

Aplicar la formula:

P = (p, α) = [p Cos(α); p Sen(α)]

Sustituir;

A= (5,45°) = [5 Cos(45°); 5 Sen(45°)]

A(5√2/2; 5√2/2)

B = (2, 160°) = [2 Cos(160°); 2 Sen(160°)]

B(-1.88; 0.68)

C = (4, 200°) = [4 Cos(200°); 4 Sen(200°)]

C(-3.76; -1.37)

D = (1, 300°) = [1 Cos(300°); 1 Sen(300°)]

D(1/2; -√3/2)

E = (3, 1.4π)

De radianes a grados;

1.4π × 180/π = 252°

= [3 Cos(252°); 3 Sen(252°)]

E(-0.92; -2.85)