Respuesta :

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

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The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

[tex]csc (\theta)=\frac{33}{55}[/tex]

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:

[tex]sin(\theta)=\frac{55}{33}[/tex]

3) So, remembering operations with fractions then the cosecant is:

[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]

[tex]csc (\theta)=\frac{33}{55}[/tex]

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