Question

In a right triangle, theta is an acute angle and sin theta = 4/9. What is the

csc theta for this same triangle?

Answer 1

`\displaystyle \csc \theta = (9)/(4)`

General Formulas and Concepts:
Trigonometry

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

Explanation:

Step 1: Define

Identify.

`\displaystyle \sin \theta = (4)/(9)`

Step 2: Find

1. Substitute in variables [Cosecant]:
   
   `\displaystyle \csc \theta = (1)/((4)/(9))`
2. Simplify:
   
   `\displaystyle \csc \theta = (9)/(4)`

∴ the cosecant of angle θ is equal to 2.25.

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Topic: Trigonometry