Respuesta :

Space

Answer:

[tex]\displaystyle \csc \theta = \frac{9}{4}[/tex]

General Formulas and Concepts:
Trigonometry

  • [Right Triangles Only] sinθ = opposite over hypotenuse
  • [Right Triangles Only] cscθ = 1/sinθ = hypotenuse over opposite

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \sin \theta = \frac{4}{9}[/tex]

Step 2: Find

  1. Substitute in variables [Cosecant]:
    [tex]\displaystyle \csc \theta = \frac{1}{\frac{4}{9}}[/tex]
  2. Simplify:
    [tex]\displaystyle \csc \theta = \frac{9}{4}[/tex]

∴ the cosecant of angle θ is equal to 2.25.

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Topic: Trigonometry

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