1=sin(90-θ)-0.075cos(90-θ)

Solución

1 = sin (9 0^{\circ} - θ) - 0.075 cos (9 0^{\circ} - θ)

θ = - 0.14971 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} n

Pasos de solución

1 = sin (9 0^{\circ} - θ) - 0.075 cos (9 0^{\circ} - θ)

Sumar

0.075 cos (9 0^{\circ} - θ)

a ambos lados

sin (9 0^{\circ} - θ) = 1 + 0.075 cos (9 0^{\circ} - θ)

Elevar al cuadrado ambos lados

sin^{2} (9 0^{\circ} - θ) = (1 + 0.075 cos (9 0^{\circ} - θ))^{2}

Re-escribir usando identidades trigonométricas

cos^{2} (θ) = (1 + 0.075 sin (θ))^{2}

Restar

(1 + 0.075 sin (θ))^{2}

de ambos lados

cos^{2} (θ) - 1 - 0.15 sin (θ) - 0.005625 sin^{2} (θ) = 0

Re-escribir usando identidades trigonométricas

- 0.15 sin (θ) - 1.005625 sin^{2} (θ) = 0

Usando el método de sustitución

sin (θ) = - \frac{0.3}{2.01125}, sin (θ) = 0

sin (θ) = - \frac{0.3}{2.01125} : θ = arcsin (- \frac{0.3}{2.01125}) + 36 0^{\circ} n, θ = 18 0^{\circ} + arcsin (\frac{0.3}{2.01125}) + 36 0^{\circ} n

sin (θ) = 0 : θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Combinar toda las soluciones

θ = arcsin (- \frac{0.3}{2.01125}) + 36 0^{\circ} n, θ = 18 0^{\circ} + arcsin (\frac{0.3}{2.01125}) + 36 0^{\circ} n, θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Verificar las soluciones sustituyendo en la ecuación original

θ = arcsin (- \frac{0.3}{2.01125}) + 36 0^{\circ} n, θ = 36 0^{\circ} n

Mostrar soluciones en forma decimal

θ = - 0.14971 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} n

- 6 sin (θ) = - 32

cos (x) = \frac{4 ( \frac{1}{2} ) - 1}{3}

sin (x) = \frac{π}{4} + \frac{0 π}{2}

cos (2 x) - sin (x) - 1 = 0

cos (x) = \frac{5}{20}