Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Ejercicio de ecuaciones trigonométricas Necesitamos el resultado del ejercicio, alfa, teta y la comprobación de cada una. Ayudaaa!! 25 cos^2⁡x=16 sin^2⁡x+32 sin⁡x+16

Sagot :

abidemiokin

Respuesta:

x = 270 grados

Explicación paso a paso:

Dada la expresión de trigonometría

25 cos ^ 2⁡x = 16 sin ^ 2⁡x + 32 sin⁡x + 16

Recuerde que cos²x + sen²x = 1

cos²x = 1-sen²x

Sustituir en la ecuación original

25 (1-sen²x) = 16 sen²x + 32 sen⁡x + 16

Expandir

25 - 25 sen²x = 16 sen²x + 32 senx + 16

16 sen²x + 25 sen²x + 32 senx + 16 - 25 = 0

41 sen²x + 32 senx - 9 = 0

Sea P = senx

41P² + 32P - 9 = 0

Factorizar

41P² + 41P -9P- 9 = 0

41P (P + 1) -9 (P + 1) = 0

(41P-9) (P + 1) = 0

41P = 9 y P = -1

Si P = -1

sinx = -1

x = arcosen (-1)

x = -90

ya que el pecado es negativo en el tercer cuadrante;

x = 180 + theta

x = 180 + 90

x = 270 grados

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.