Cali4812 Cali4812
  • 13-11-2019
  • Mathematics
contestada

If sin ⁡x=7/25, and 0 < x < π/2, what is cos⁡(x−3π/2)?

Respuesta :

steffaniasierrag
steffaniasierrag steffaniasierrag
  • 16-11-2019

Answer:

[tex]Cos(x-\frac{3\pi}{2})=-\frac{7}{25}[/tex]

Step-by-step explanation:

Remember that [tex]cos(x-y)=cos(x)cos(y)+sin(x)sin(y)[/tex]

Then,

[tex]cos(x-\frac{3\pi}{2})=cos(x)cos(\frac{3\pi}{2})+sin(x)sin(\frac{3\pi}{2})\\[/tex]

But [tex]cos(\frac{3\pi}{2})=0[/tex] and [tex]sin(x)=\frac{7}{25}[/tex]

Then

[tex]cos(x-\frac{3\pi}{2})=cos(x)*0+\frac{7}{25}*sin(\frac{3\pi}{2})\\=\frac{7}{25}*(-1)=\frac{-7}{25}[/tex]

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