Question

use a graphing calculator to evaluate. round to 3 decimal places.
\\( \sec \left(260^{\circ}\
ight)= \\)
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question 14
use a graphing calculator to evaluate. round to 3 decimal places.
\\( \csc \left(126^{\circ}\
ight)= \\)
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Explanation:

Step1: Recall the reciprocal identities

We know that \(\sec\theta=\frac{1}{\cos\theta}\) and \(\csc\theta = \frac{1}{\sin\theta}\)

For \(\sec(260^{\circ})\):

Since \(\sec(260^{\circ})=\frac{1}{\cos(260^{\circ})}\)
Using a graphing calculator in degree mode, \(\cos(260^{\circ})\approx - 0.1736481777\)
Then \(\sec(260^{\circ})=\frac{1}{\cos(260^{\circ})}\approx\frac{1}{- 0.1736481777}\approx - 5.759\)

For \(\csc(126^{\circ})\):

Since \(\csc(126^{\circ})=\frac{1}{\sin(126^{\circ})}\)
Using a graphing calculator in degree mode, \(\sin(126^{\circ})\approx0.8090169944\)
Then \(\csc(126^{\circ})=\frac{1}{\sin(126^{\circ})}\approx\frac{1}{0.8090169944}\approx1.236\)

Answer:

\(\sec(260^{\circ})\approx - 5.759\)
\(\csc(126^{\circ})\approx1.236\)