(50.691)cos(50.691-c)+sin(50.691-c)=0

Solución

(50.691) cos (50.69 1^{\circ} - c) + sin (50.69 1^{\circ} - c) = 0

c = - 0.70579 \dots + 18 0^{\circ} n

Pasos de solución

(50.691) cos (50.69 1^{\circ} - c) + sin (50.69 1^{\circ} - c) = 0

Restar

sin (50.69100 \dots^{\circ} - c)

de ambos lados

50.691 cos (0.88472 \dots - c) = - sin (- c + 50.69100 \dots^{\circ})

Elevar al cuadrado ambos lados

(50.691 cos (0.88472 \dots - c))^{2} = (- sin (- c + 50.69100 \dots^{\circ}))^{2}

Re-escribir usando identidades trigonométricas

2569.577481 (0.63350 \dots cos (c) + 0.77374 \dots sin (c))^{2} = sin^{2} (- c + 50.69100 \dots^{\circ})

Restar

sin^{2} (- c + 50.69100 \dots^{\circ})

de ambos lados

2569.577481 (0.63350 \dots cos (c) + 0.77374 \dots sin (c))^{2} - sin^{2} (- c + 0.88472 \dots) = 0

Factorizar

2569.577481 (0.63350 \dots cos (c) + 0.77374 \dots sin (c))^{2} - sin^{2} (- c + 0.88472 \dots) : (50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) + sin (- c + 0.88472 \dots)) (50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) - sin (- c + 0.88472 \dots))

(50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) + sin (- c + 0.88472 \dots)) (50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) - sin (- c + 0.88472 \dots)) = 0

Resolver cada parte por separado

50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) + sin (- c + 0.88472 \dots) = 0 or 50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) - sin (- c + 0.88472 \dots) = 0

50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) + sin (- c + 0.88472 \dots) = 0 : c = arctan (- 0.85224 \dots) + 18 0^{\circ} n

50.691 (0.63350 \dots cos (c) + 0.77374 \dots sin (c)) - sin (- c + 0.88472 \dots) = 0 : c = arctan (- 0.78632 \dots) + 18 0^{\circ} n

Combinar toda las soluciones

c = arctan (- 0.85224 \dots) + 18 0^{\circ} n, c = arctan (- 0.78632 \dots) + 18 0^{\circ} n

Verificar las soluciones sustituyendo en la ecuación original

c = arctan (- 0.85224 \dots) + 18 0^{\circ} n

Mostrar soluciones en forma decimal

c = - 0.70579 \dots + 18 0^{\circ} n

sec (4 θ) = 2

tan^{2} (x) - 4 tan (x) + 1 = 0

sec (θ) + cos (θ) = sin (θ) tan (θ)

cos (x) = 0.98

tan (3 x + \frac{π}{2}) = - 1