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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

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