Transforma las coordenadas rectangulares de las siguientes vectores a coordenadas polares
Respuestas
De la transformación de las coordenadas rectangulares a coordenadas polares se obtiene:
1. (x, y) = [2√745 · Cos(28.44°); 2√745 · Sen(28.44°)]
2. (x, y) = [10√754 · Cos(-33.11°); 10√754 · Sen(33.11°)]
3. (x, y) = [26√17 · Cos(-53.34°); 26√17 · Sen(-53.34°)]
4. (x, y) = [124 · Cos(52.2°); 124 · Sen(52.2°)]
5. (x, y) = [50√10 · Cos(18.43°); 50√10 · Sen(18.43°)]
6. (x, y) = [3605.55 · Cos(-56.3°); 3605.55 · Sen(-56.3°)]
7. (x, y) = [43.93 · Cos(-41.3°); 43.93 · Sen(-41.3°)]
8. (x, y) = [340√2 · Cos(45°); 340√2 · Sen(45°)]
Explicación:
Para trasformar las coordenadas cartesianas a polares, por medio de relación:
(x, y) = [r · Cos(θ); r · Sen(θ)]
siendo;
- r = √(x²+y²)
- θ = Tan⁻¹(y/x)
1. x = -48; y = -26
θ = Tan⁻¹(-26/48) = 28.44°
r = √(48²+26²) = 2√745
Sustituir;
(x, y) = [2√745 · Cos(28.44°); 2√745 · Sen(28.44°)]
2. x = 230; y = -150
θ = Tan⁻¹(-150/230) = -33.11°
r = √(230²+150²) = 10√745
Sustituir;
(x, y) = [10√754 · Cos(-33.11°); 10√754 · Sen(33.11°)]
3. x = -64; y = 86
θ = Tan⁻¹(86/-64) = -53.34°
r = √(64²+86²) = 26√17
Sustituir;
(x, y) = [26√17 · Cos(-53.34°); 26√17 · Sen(-53.34°)]
4. x = 76; y = 98
θ = Tan⁻¹(98/76) = 52.2°
r = √(76²+98²) = 124
Sustituir;
(x, y) = [124 · Cos(52.2°); 124 · Sen(52.2°)]
5. x = -150; y = -50
θ = Tan⁻¹(-50/-150) = 18.43°
r = √(150²+50²) = 50√10
Sustituir;
(x, y) = [50√10 · Cos(18.43°); 50√10 · Sen(18.43°)]
6. x = 2000; y = -3000
θ = Tan⁻¹(-3/2) = -56.3°
r = √(2000²+3000²) = 3605.55
Sustituir;
(x, y) = [3605.55 · Cos(-56.3°); 3605.55 · Sen(-56.3°)]
7. x = -33; y = 29
θ = Tan⁻¹(29/-33) = -41.3°
r = √(33²+29²) = 43.93
Sustituir;
(x, y) = [43.93 · Cos(-41.3°); 43.93 · Sen(-41.3°)]
8. x = 340; y = 340
θ = Tan⁻¹(1) = 45°
r = √(340²+340²) = 340√2
Sustituir;
(x, y) = [340√2 · Cos(45°); 340√2 · Sen(45°)]