Question

Transforma las coordenadas rectangulares de las siguientes vectores a coordenadas polares

Answer 1

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°)]