129.8sin(a)-0.6129.8cos(a)=121.79

Solución

12 \cdot 9.8 \cdot sin (a) - 0.6 \cdot 12 \cdot 9.8 \cdot cos (a) = 12 \cdot 1.79

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

Pasos de solución

12 \cdot 9.8 sin (a) - 0.6 \cdot 12 \cdot 9.8 cos (a) = 12 \cdot 1.79

Sumar

0.6129.8 cos (a)

a ambos lados

117.6 sin (a) = 21.48 + 70.56 cos (a)

Elevar al cuadrado ambos lados

(117.6 sin (a))^{2} = (21.48 + 70.56 cos (a))^{2}

Restar

(21.48 + 70.56 cos (a))^{2}

de ambos lados

13829.76 sin^{2} (a) - 461.3904 - 3031.2576 cos (a) - 4978.7136 cos^{2} (a) = 0

Re-escribir usando identidades trigonométricas

13368.3696 - 18808.4736 cos^{2} (a) - 3031.2576 cos (a) = 0

Usando el método de sustitución

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472}, cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472}

cos (a) = - \frac{3031.2576 + 1014943029.424128}{37616.9472} : a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn

cos (a) = \frac{1014943029.424128 - 3031.2576}{37616.9472} : a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Combinar toda las soluciones

a = arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn, a = 2 π - arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Verificar las soluciones sustituyendo en la ecuación original

a = - arccos (- \frac{3031.2576 + 1014943029.424128}{37616.9472}) + 2 πn, a = arccos (\frac{1014943029.424128 - 3031.2576}{37616.9472}) + 2 πn

Mostrar soluciones en forma decimal

a = - 2.75844 \dots + 2 πn, a = 0.69769 \dots + 2 πn

sin (x) (sin (x) - 1) = 5 cos^{2} (x) - 4

v, a = arctan (\frac{v ^{2}}{g R})

3 sin^{2} (x) = 4 sin (x)

5 sin (θ) = 4

2 cos^{2} (x) - 7 cos (x) = 0