Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.