Question

question
if θ is an angle in standard position and its terminal side passes through the point (9, 2), find
the exact value of csc θ in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Calculate the distance \( r \) from the origin to the point \((9,2)\)

Use the distance formula \( r=\sqrt{x^{2}+y^{2}} \), where \( x = 9 \) and \( y = 2 \).

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Step2: Recall the definition of \( \csc\theta \)

By the definition of trigonometric functions in the coordinate plane, \( \csc\theta=\frac{r}{y} \).
Since \( r = \sqrt{85} \) and \( y=2 \), then \( \csc\theta=\frac{\sqrt{85}}{2} \)

Answer:

\(\frac{\sqrt{85}}{2}\)