Question

Use the appropriate reciprocal identity to find the exact value of sin for the given value of csc . Rationalize denominators when applicable. csc 27/5 sin

Answer 1

`\sin(\theta) = (5)/(27)`

Explanation:

Given

`\csc(\theta) = (27)/(5)`

Required

Determine
`\sin(\theta)`

In trigonometry identity;

`\sin(\theta) = (1)/(\csc(\theta))`

So, we have:

`\sin(\theta) = (1)/((27)/(5))`

Take inverse of the fraction

`\sin(\theta) = (5)/(27)`