Question

let \\((-6, 5)\\) be a point on the terminal side of \\(\theta\\).
find the exact values of \\(\sin \theta\\), \\(\csc \theta\\), and \\(\cot \theta\\).

\\(\sin \theta = \\)
\\(\csc \theta = \\)
\\(\cot \theta = \\)

Explanation:

Identify coordinates and calculate distance

Using the Coordinate Plotting knowledge point

$$
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$$

Determine sine value

Using the Exact Values knowledge point

$$ \sin\theta = \frac{y}{r} = \frac{5}{\sqrt{61}} = \frac{5\sqrt{61}}{61} $$

Determine cosecant value

Using the Exact Values knowledge point

$$ \csc\theta = \frac{r}{y} = \frac{\sqrt{61}}{5} $$

Determine cotangent value

Using the Exact Values knowledge point

$$ \cot\theta = \frac{x}{y} = -\frac{6}{5} $$

Answer:

Let \((-6, 5)\) be a point on the terminal side of \(\theta\). Find the exact values of \(\sin \theta\), \(\csc \theta\), and \(\cot \theta\).

\(\sin \theta =\) <blank>\(\frac{5\sqrt{61}}{61}\)</blank>

\(\csc \theta =\) <blank>\(\frac{\sqrt{61}}{5}\)</blank>

\(\cot \theta =\) <blank>\(-\frac{6}{5}\)</blank>